A number of people have pointed out that Matthew seems to specifically link the healing miracles of Jesus to his title as "Son of David." Some examples:
9:27 – As Jesus went on from there, two blind men followed him, calling out, "Have mercy on us, Son of David!"
12:22-23 – Then they brought him a demon-possessed man who was blind and mute, and Jesus healed him, so that he could both talk and see. All the people were astonished and said, "Could this be the Son of David?"
15:22 – A Canaanite woman from that vicinity came to him, crying out, "Lord, Son of David, have mercy on me! My daughter is suffering terribly from demon-possession."
20:30 – Two blind men were sitting by the roadside, and when they heard that Jesus was going by, they shouted, "Lord, Son of David, have mercy on us!"
I can't remember David ever performing any healing miracles, so where does this connection come from and why does Matthew make it?
It looks like there are a couple JSTOR papers out there on this topic, but I don't have access to them. In the abstract one seems to suggest Ezekiel 34 for a possible background, but also seems to mention that there are other ideas.