I guess it might be individual but at least for me I can't remember the weight of the glasses ever bothering me. Sort of seeing them in the corners of my eyes did initially annoy me, I think, but not for long.
That said, after wearing glasses for like 25 years I'm still both a little annoyed when they're dirty and a little too lazy to regularly clean them properly (in my defense, it seems to take roughly five minutes until they're at least a little dirty again).