So much could be said about this reading it is difficult to know where to start! Here I want to highlight Jesus' role as the Davidic healer.
Healing and the Eschatological/Messianic Age
The story of the healing of Bartimaeus clearly links Jesus’ role as healer to his identity as the Son of David. In fact, all of the Gospels link Jesus’ ability to heal to his role as the Davidic messiah (cf. Matt 9:27; 20:31; Mark 10:48; Luke 18:38–39). Indeed, a number of prophetic texts, Second Temple sources and later rabbinic writings specifically associate the arrival of the eschatological age with the idea of healing. Here I will only list a few:
Isa 29:18: “In that day the deaf shall hear the words of a book, and out of their gloom and darkness the eyes of the blind shall see.”
Isa 35:5: “Then the eyes of the blind shall be opened, and the ears of the deaf unstopped; 6 then shall the lame man leap like a hart, and the tongue of the dumb sing for joy.”
Numerous other biblical texts could also be cited (cf. Isa 19:22; 30:26; 53:5; 57:18–19; 58:7; Jer 30:17; 33:6; Ezek 47:12; Hos 6:1; 7:1; Mal 4:2). In addition, the eschatological age is also linked with healing in non-biblical Second Temple sources.
Jubilees 23:29–30: “And all of their days they will be complete and live in peace and rejoicing and there will be not Satan and no evil (one) who will destroy, because all of their days will be days of blessing and healing. And then the Lord will heal his servants, and they will rise up and see great peace.”
1 Enoch 96:3: “But you, who have experienced pain, fear not, for there shall be a healing medicine for you.”
One particular text is worth mentioning here. One of the Dead Sea Scrolls, 4Q521, which draws from the passage from Isaiah 35 cited above and links it with Isaiah 61, reveals that the Messiah will be a healer. The fragment begins: “1 [for the heav]ens and the earth will listen to his anointed one, 2 [and all th]at is in them will not turn away from the precepts of the holy ones. . .” The fragment then continues to explain that the Lord
“will honour the pious upon the throne of an eternal kingdom, freeing prisoners, giving sight to the blind, straightening out the twis[ted.]… And the Lord will perform marellous acts such as have not existed just as he sa[id,] [for] he will heal the badly wounded and will make the dead live, he will proclaim good news to the poor and […]…[…] he will lead […] … and enrich the hungry.” (4Q521 2 II, 7 and 11-13).
Jesus' Role as the Healer Messiah
The tradition linking healing to the eschatological age is especially present in Matthew and Luke, where Jesus appeals to his ability to heal lepers as evidence that he is the Messiah. One particularly important passage is found in both Matthew and Luke. When John the Baptist’s disciples come asking him whether he is “the one to come,” Jesus states, “the blind receive their sight and the lame walk, lepers are cleansed and the deaf hear, and the dead are raised up, and the poor have good news preached to them” (Matt 11:5//Luke 7:22). As is well-known, in this saying Jesus conflates Isaiah 35 and 61, mirroring 4Q521. Strikingly, both the Qumran text and Jesus insert a statement about raising the dead prior to the task of preaching to the poor.
Jesus' Role As the Davidic Healer
Of course, the Gospels link Jesus’ role as healer precisely to his role as the Davidic messiah. What is interesting about this is that there really is no clear pre-Christian text describing the Davidic messiah as a healer. There is at least one text that should be mentioned here: Ezekiel 34. There the Lord promises to help the sheep who are weak and crippled (cf. Ezek 34:4, 16) within the same context in which he promises to send a Davidic Messiah (cf. Ezek 34:23–24). But even here the connection is rather ambiguous.
So how did Jesus’ role as healer come to be associated with his role as the eschatological Son of David? Well, certainly given the fact that the messiah was already linked with healing in 4Q521 it is not surprising that Jesus’ role as the Davidic Messiah would be connected with his healing. Yet we might also point out that the ink could have been established in connection with the fact that David was remembered for having exorcistic and healing abilities (cf. 1 Sam 16:14–23; Josephus, A.J. 166–68; 11QPsa XI, 2–11; L. A. B. 60:1). Even more descriptive are the numerous texts relating Solomon’s abilities as an exorcist and healer (cf. Josephus, A.J. 8:42–49; Apoc. Adam 7:13; cf. also Wis 7:20). It is therefore easy to see how Jesus’ healing abilities could have been linked with his exorcistic powers and how these together could be have been linked with his role as the eschatological “Son of David.”
In fact, as Meier explains, that a Solomonic reference is present here is strongly suggested by the fact that, with the exception of one occurrence where it is linked with Absalom (cf. 2 Sam 13:1), the term “Son of David” is normally used as a referent to Solomon (cf. 1 Chron. 28:22; 2 Chron 1:1; 13:6; 30:26; 35:3; Prov 1:1; Eccl 1:1).  In light of this Bartimaeus cry is not at all surprising―“Have mercy on me, Son of David!”
 See also Apocalypse of Moses 2:275. For an excellent overview of biblical texts dealing with healing, see Michael L. Brown, Israel’s Divine Healer (SOTBT; Grand Rapids: Zondervan, 1995); Lidija Novakovic, Messiah, the Healer of the Sick: A Study of Jesus as the Son of David in the Gospel of Matthew (WUNT 2.170; Tübingen: Mohr Siebeck, 2003), 152–83.
 Novakovic (Messiah, the Healer of the Sick, 180) writes: “In contrast to the Jewish texts which are only thematically related to 4Q521, the Q passage preserved in Matt 11:2–6 and Luke 7:18–23 contains the closest known parallel to this document, because both texts go beyond their common scriptural basis in Isa 61:1 by adding the reference to the resurrection of the dead in front of the reference to preaching good news to the poor.” Likewise see M. O. Wise and J. Tabor, “4Q521 ‘On Resurrection’ and the Synoptic Gospel Tradition: A Preliminary Study,” JSP 10 (1992) 161 [149–62]: “Although it is unlikely that Luke knew the Qumran text directly, it seems that he shares with its author a common set of messianic expectations.”
 Puesch has argued that the messianic figure in 4Q521 is a royal messianic figure, finding a reference to a “scepter” in 4Q521 2 III, 6. However, the text is unclear. See Émile Puech, “Une apocalypse messianique (4Q521),” RQ 15/60 (1992): [475-522]; Collins, “The Works of the Messiah,” 103. See also David Aune, “The Problem of the Messianic Secret,” NovT 11 (1969): 39 [1–31]. We might also mention L.A.B. 60:3, where the exorcistic song sung by David has him telling the evil spirit, “But let the new womb from which I was born rebuke you, from which after a time one born from my loins will rule over you”. The passage is admittedly obscure. In favor of a messianic reading is the fact that the language bears close similarities to 2 Sam 7:11 (LXX), which is cited as a messianic prophecy in 4Q174. The passage also echoes Psalm 132:11 (LXX) and T. Levi 18:12, which may also signal messianic hopes. For those who advocate such an approach see Dennis C. Duling, “Solomon, Exorcism, and the Son of David,” HTR 68 (1975): 240; Paul Riessler, Altjüdisches Schrifttum ausserhalb der Bibel, übersetzt und erläutert (2d ed; Darmstadt; Wissenschaftliche Buchgesellschaft, 1966), 1318; Marc Philonenko, “Remarques sur un hymne essénien de caractère gnostique,” Sem 11 (1961): 52 [43–53].
 Especially important is the combination in Josephus’ account of Solomon’s exorcistic abilities with his role as healer (cf. A.J. 8.45: “[He was enabled] to help and heal human beings”). See also the discussion in Meier, A Marginal Jew, 2:689. In addition, see the exorcistic connections made with Solomon in the Aramaic magical texts discussed by Loren Fisher, “Can This Be the Son of David?,” in Jesus and the Historian: Written in Honor of Ernest Cadman Colwell (ed. F. T. Trotter; Philadelphia: Westminster, 1968), 82–97; J. A. Montgomery, Aramaic Incantation Texts from Nippur (Philadelphia: The University Musueum, 1913), 232; Cyrus H. Gordon, “Aramaic Magical Bowls in the Instanbul and Baghdad Museums,” ArOr 6 (1934): 319–34, 466–74; C. D. Isbell, Corpus of the Aramaic Incantation Bowls (SBLDS 17; Missoula, Mont.; Scholars Press, 1975), 108-111, 114-115.
 Meier, A Marginal Jew, 2:737 n. 47. explains that a Solomonic reference is strongly suggested by the fact that, with the exception of one occurrence where it is linked with Absalom (cf. 2 Sam 13:1), the term “Son of David” was regularly used for Solomon (cf. 1 Chron. 28:22; 2 Chron 1:1; 13:6; 30:26; 35:3; Prov 1:1; Eccl 1:1; cf. also Fisher, “Can This Be the Son of David?,” 90). See the discussion in Duling, “Solomon, Exorcism, and the Son of David,”235–52; idem., “The Therepeutic Son of David: An Element in Matthew’s Christological Apologetic,” NTS 24 (1977-78): 392–410.