Way to completely mis-use the info you have on him. He bets river 100% vs missed cbets (so at least he knows how to bluff when people have given up), and now he check/jams. He has it. Fold.

And not betting this turn is way worse than you think. Your hand may be face-up to CO, but you're not getting any money from him anyway, it's SB you're after, who can have a ton of draws & worse Kx and even like TT.

He actually made max value playing his hand this way.

Cant believe that someone checking 3 times would actually fool you. OF COURSE he has you crushed. This is what players running 41/1 do.
Its like it Amazes me when a fish limps in preflop, we raise with JJ, then fish shoves & we snap call only to go OMG "how could you play aces like that". Thats what they do with monsters- they slowplay them and hope you hit something.

Why are we focusing on the checking and ignoring the fact he just shoved?

So if this was on Cake then you didn't have time to look up their check raise river stat but if you knew it was 22% then you need a call on your bet 22% because you have to fold to every check raise. You beat kj and kt ... maybe kxs which might call and are around 50 combos versus the hundreds of combos of random trash that would fold. So I wouldn't even bet the river, only the turn to get draws to call and defend against 2 out PP.
Bottom line is this, the fish don't want to get small value only big buy- in type value and they do it by waiting until the river to overbet.

And I would like to add,I don't think its a smart decision risking your whole stack over a top pair,top kicker.