"Weigh" is the normal phrase meaning to evaluate, but things can be "weighted" as well. As in a weighted average. This is to assign higher priorities (weights) to different factors in a decision/calculation.
So "to weight certain arguments" would mean to give them more importance than some other arguments?
weigh arguments = evaluate/assess arguments
weight arguments = give priority/importance to arguments
If you have a question about the English language and would like to ask one of our many English teachers and language experts, please click the button below to let us know: