Interesting spot with KTs 200bb deep

Hero $600 - been playing pretty straight forward - not showing down any garbage, and did lose a few hands getting coolered where I flopped the nuts and got out drawn but all the money went in on the flop.

Villian - $500 - Older lady who hasn't gotten out of line too much. She did 3b to $80 with 99 over a bunch of over callers of a $12 open which I did not think she would show up with that, but not out of line - but she did play pretty passively after the flop.

I get K♣T♣ in the HJ and she goes $15 from UTG+1
I like 3b or call here but I choose call because it was a 5bb open
BTN over calls with a $100 stack (this guy plays way too many hands)

$48~
T♥5♦4♣

She goes $40
I had some alarm bells going now because of the sizing but I don't see how I could possibly fold
BTN over calls too which is kinda annoying

$168
Turn 3♣
She checks
Hero???

I wasn't sure if I should just check back - getting check raised here would be a disaster but I could set up a pretty nice bet/bet and get her off an over pair.