I think what Belichik is doing is threatening Welker and trying to brand him as a “dirty player”. He is trying to make him unpopular, He is trying and to get him fined and trying to hurt his career. He also may be saying I am going to instruct my players that you are dirty and to take you out the next time we play.
The Patriots treated Welker badly. They refused to give him a contract. They refused to pay him what he was worth. They forced him to leave. Welker was Tom Brady's close friend and his favorite receiver. I believe Welker said one of the reasons he left the Patriots was because of Belichik.
Belichik has a history of this. He also forced out Deion Branch the Superbowl MVP.
You could argue however, that part of the Patriots’ success is not being sentimental, and going ahead and letting go of players right before their downward slide.