Only Jesus has the power to cure us on earth. Scripture tells us that the prayer of a righteous man is worth much. Who is more righteous than those perfectly united with Jesus in heaven? We all know that we are parts of the body of Christ and the entire body has a role to play. Christ, as the head of the body, is in control.
When we say that, St. Lucy, for example, cured my eye sight, we are saying that we asked St. Lucy to intercede on our behalf to Jesus. Jesus hears our prayer first and passes that request to St. Lucy. Jesus already knows what we need because in asking for the help of a saint, we ask for Jesus’s help too.
Let’s say you are sued. You retain a lawyer to intercede for you to the judge. The lawyer does a good job and the judge relents and drops the charges. When you tell your friends the good news, do you say that ‘Judge X dropped the charges!’ Or do you say, ‘That my lawyer got the charges dropped!’. Most people do the latter. It is the judge who actually drops the charges, but it was because your lawyer went to bat for you. You will probably recommend that same lawyer to a friend if they land in the same mess.
It should always be the Catholic understanding that without Christ, nothing happens. No saint is greater than Jesus. We acknowledge the saint for their work on our behalf and we praise Jesus for curing us.
Hope this helps!