'Weigh in' is a phrasal verb which means to make a significant contribution to a discussion or an argument. (As a noun, a 'weigh-in' is the official weighing of something or someone before a race or competition) This phrasal verb is usually used in professional contexts.

1. I actually have quite a bit of past experience with the problem you are discussing, so do you mind if I weigh in here and offer some advice?
2. The politician weighed in on the debate about gun crime with his own, impassioned plea for stricter regulation. 

1. Please be quiet during this meeting, we could do without you weighing in with your forceful opinions.