Do we have 9d? That's pretty relevant here; having it takes a bunch of pair+draw hands out of V's range.
The fact that he opened K9o means he can take this line with a few weaker value hands (Q9, 33), and can have a few combo draws or even Axd, so I can't imagine folding here. His sizing is also weird; he's making it clearly correct for our combo draws to call. Problem is calling kinda sucks because we hate half the deck and still have >PSB behind, and 4b is really thin if he has a fold button. In the moment, I probably flat and gii on most turn cards, but a small 4b for value with the intention to gii on the turn might be better, since flatting allows him to get away too easily from weaker hands on a bunch of possible turn cards.
Playing against an unknown 560bb deep is hard