Sup waffles, I can give you my thoughts on this hand but I may not have the best advice.
There's going to be a lot of people that would disagree with your preflop call, and in most situations I'd disagree as well. However, with the table dynamics as they are, I don't mind taking a flop and seeing what develops. I think I would take a hand with a bit more equity, like KTs to make the call, but KTo is still okay.
I see a lot of strange preflop plays at the 1/2 tables, (I've been playing those stakes for the past two months). The $20 minraise is actually extremely common, as I've encountered. People don't tend to raise to get people out of the pot or as a bluff, they just blindly do it if they like their hand, which happens to be the case here. Online, I would worry a lot about the minraise meaning significant strength, but people are just so oblivious to sizings in live games, so it really doesn't mean much. Sorry for the rant there.
Anyways, the flop call and the turn check are both totally standard plays, so nothing to worry about there. Once you see the villain check the turn, it is really open to interpretation. This check can mean she turned the stone nuts, is giving up, or has marginal showdown value.
On the river, when she checks to you she is VERY unlikely to have the goods. Especially considering you checked back the turn. In my opinion, this is the perfect bet size by you for this situation. She will occasionally have KJ but is much more likely to have 99-QQ.
You really shouldn't be worried about a better kicker on this river, I think KJ-AK would almost always bet the river after you check back the turn. There's really no reason for them to bloat the pot with one pair, but some people do tend to overvalue AK.
The hands she is repping with her checkraise on the river are 33, 44, 88, KK, maybe AK and that's about it. Maybe she has some weird 34s that decided to raise pre, but I think that's extremely unlikely as played. Just think how you would have played those hands in her shoes.
Personally I don't think your river call is stupid at all, I would have played the hand the exact same if I decided to flat the raise with KT.
NH and hope this helps