Yeah, we use weathering all the time. Just the context here sounds weird to my ears. Weathering what? Or are they weathering themselves? It makes me think of some old statues dissolving in the rain!?
These days ‘I’m lovin’ it’ sounds perfectly normally to me. At the time the advert was introduced however, it sounded really odd. I guess that shows the dynamic nature of language!
I don’t think its ‘correct’ English though. I think love is a stative verb so you would say ‘I love it’. I don’t think anybody ever really said ‘I’m loving it’ before the advert. At least in the UK. Just like you wouldn’t normally say ‘I’m believing it’.