One of my villagers is considerably older than she was before and is 2 years older than what used to be the eldest villager. The last time I checked, she was either 48 or 49, and now she is 51.

I have also used Time Warp on her a couple of times. Does Time Warp increase your age faster, or is the reason something else?

I think it does make people age faster. I time warped someone a few times and it aged them a year.