Private schools are mostly from 5th grade on, and usually children attend the elementary school which is closest to their home. If you want to change school, you'll need a good reason to send your son out of the catchment area. Sending him to a private school is a good reason, some parents say their child lives with grandma now and attends school there. You could move, but all this is very difficult if you have no family close-by.
There is a Montessori school in Weinheim, but I don't know anything about it. The private MIS in Viernheim gets very mixed reviews. I used to know a family whose daughter attended it, they were more than happy. This was several years ago, though, and from what I hear now, the school has got worse. There are some posts about it here.
Maybe you can continue trying to improve the situation at your son's current school. A lot depends on the teacher, some go out of their way to help the children, others don't bother at all. Have you talked to the Elternbeirat yet? How is your son's teacher seen by the other parents? How good is your son's German? Does he get extra tutoring in the afternoon? Either in one of the Nachhilfeschulen or by a private tutor? If you can get someone who knows your son's school, it'll help him a lot. What about his friends' parents? Have you talked to them about the situation?
Good luck to you and your son.