I don't think you can do much on the visitation weekends, but you do not have to let him go to meetings when you have him. Tell them "Thank you for your interest in my son, but I have decided it's not in his best interest to go to any Jehovah's Witness functions while he is with me." Your son is probably being influenced to ask to do those things, you can influence him also.
Whatever comes up just say you already had plans, then take your son to go do something fun at those times, work on getting him to learn critical thinking, so he can recognize the lies and deceptions that are used by the Society. Take him to a natural history museum to learn about evolution, etc.