weigh in or wade in

To weigh into a debate is to enter it forcefully, bringing one’s full weight of conviction into the discussion.  This idiom seems to be not as common as it used to be, so that, particularly in the past tense, they weighed into the debate, weighed  is being replaced by waded, at a rate of about seven to one.  To wade in has had the meaning of confronting someone, either physically or verbally. You can wade into a fight or an argument.  So to move from there to making a forceful contribution to a discussion is not a big step. 

 To my mind, you wade into a fight or an argument that is happening right in front of you. There is much greater physicality and immediate presence required. Weighing in is a much more cerebral activity, part of a civilised exchange of ideas and carried out in a debate where the parties are present or remote.