How do I get residential custody of 16 year old in WA state after 3 years of 50/50 custody?

You would need to file a petition to modify the parenting plan based upon a substantial change of circumstances since the last parenting plan was signed. Unfortunately, a 16 year old child's wishes are not determinative of the issue. The trial Judge must base his/her decision on whether or not to modify the plan on the best interests of the child. In your case, you would need to get a parenting evaluator appointed to insure that the Judge knows of the child’s wishes because testimony of children at trial is strongly discouraged and the court may not wish to hear directly from the child, hence the need for an evaluator to whom the child may express his wishes and the evaluator testifies at trial.

These issues can get very complicates so please consult with an attorney before initiating any action.

Hope this helps