P.S.
Of course he is having trouble b/c he's a mama's boy. You have set him up for failure or if anything, disappointment, in the real world, imo. All his life you have led him to believe his world is you and only you, and now you leave him w/a sitter and expect him to adjust well?
Ask your sitter if you can have a sort of "mid term" meeting. Let her know what your relationship is like w/your son. Be clear on how you treat him and then let her know you're finding out that you both (you and your son) are having a hard time adjusting to leaving him. If she is a good and wise sitter, she will know how to handle clingy mommies and kids w/love and concern and will find a way to help him adjust. But there is no way you can ask her to treat him the way you treat him.
To help your son balance 100% from you and not as much from the sitter, you are going to have to start letting him become moreindependent. Start letting him play more by himself - start w/5 mins a day. Leave some toys and books w/him and tell him to play while you go to another room. He'll whine and cry but after a week or so he should start getting used to being left alone. Then as he starts playing by himself for a certain length of time, add on a minute or two until you build up to him being able to play by himself for at least 15-20 mins. He's 3...he is well old enough to play by himself.
Do the same for when he goes to sleep, eating...anything. Let him start doing things on his own, like finding a toy or finding his shoes. Chances are the sitter expects him to do things independently and he doesn't like it, thus, the protests when you leave him.
You can teach your child independence while still being loving, caring and nurturing. gl