For instance if a woman asks the man she is seeing if she means more to him than just the "fun stuff", and he replies you matter more than just that to me, rather than you mean a lot to me? Does using the word matter lessen the sincerity rather than using the word mean? Many thanks.
I'd suggest the majority of men are not fine tuned enough in the use of the English language to consider first which word they use before they speak so don't analyse.
he's answering the question asked.
Q. Do I mean more to you than just the fun stuff?
A. You matter more than just that to me.
versus
Q How much do I mean to you.
A You mean a lot to me.
subtext
Her. I need reassurance, tell me how much you love me.