Jesus takes our illnesses and bears our diseases by taking our weaknesses upon himself (so that we no longer bear them) and by truly taking them away—both of which are included in the Greek word lambadein in Matthew 8:17. Ultimately, Jesus takes away all our sins, illnesses, and uncleannesses by taking them upon himself through his substitutionary death on the cross (1 Peter 2:24).
Jesus has taken our weaknesses upon himself so that we no longer bear them. He has borne our illnesses so that they no longer weigh us down. In other words, the text here is not simply teaching that Jesus takes our weaknesses and illnesses upon himself, but also that he truly takes them away from us. This is also what happens when he heals us (Matthew 8:16). We lose the sickness, thanks be to him.1 The Greek word lambadein which is here in Matthew 8:17 (ESV) translated simply as take
literally means to take upon himself and to take away. Jesus takes away our sins and illnesses by taking them upon himself through his substitutionary suffering and death.2 Jesus therefore takes all these illnesses upon himself, and just like he touches the unclean leper, so he also takes the uncleanness of sin upon himself, thereby redeeming his people from their unrighteousness (1 Peter 2:24).3
17 This was to fulfill what was spoken by the prophet Isaiah: “He took our illnesses and bore our diseases.”