Sin and sickness are inextricably linked. Sickness is a consequence of sin. God's righteousness demands that sin be paid for. The problem for man is that the penalty is death. We are already dead in trespass and sin. (Colossians 2:13) So we have nothing with which to pay the debt. Jesus was sinless, so He could, and did, pay the price of all the sin of all mankind.
The "stripes" is misleading. It was not a light mark like you see in the movies. Isaiah says that the back of Jesus was like a plowed field. It's not just sin in the abstract, but all the wickedness of mankind that was laid on Jesus. Jesus was hung on a cross. That was wood. from a tree. God warned Israel that they would be cursed if they turned away from Him. We know that Israel continually failed to obey. Every time they got right, they would drift back into idolatry. God put the curse due to Israel on the Lord Jesus (Galatians 3:13).
Sickness and disease afflicts the body. So the body of Jesus was afflicted.
God wants much more than forgiveness for us. People know that God hates sin, but not so many realise why. Yes, it offends God's holiness. Sin is also destructive to us as individuals. The gospel is not only going to heaven when you die. It is eternal life that begins the moment that you are born again. God breaks the power of sin by including us in the death of Christ when we believe. When we realise that we are dead to sin, we can resist temptation.
Suppose you had to appear in court for a serious crime. While on remand, you pass away. Will the court case proceed? No. That would be stupid. So God no longer has a case against you.
On the positive side, God includes us in the resurrection of Jesus also. He raises us up to be new creations. We now have the power, in Christ, to live righteously. Satan will often try to remind us of our past sins and failures. Agree with him! But also remind him that he is talking about a dead man.
If we can get this great truth into our hearts, it will change our lives. We really are new creations in Christ. He really does live in us to be all that God demands that we must be. The old really has passed away and the new really has come. Everything we've learned, how we feel and our thoughts argue against this great truth. Let God's word be your absolute authority. Study His word diligently so that the truth can set you free. Ask God to make things clear to you. He delights to reveal Himself to those who seek Him.