[Qgel]

His most likely hands to get to this river are JJ and QQ and after those, KK. So now it all simply comes down to whether you think he can call here with QQ/JJ at least half the time. It's very hard to know that for sure without any specific reads. Is he the type of nit who is scared of everything postflop or is he a thinking postflop player who can read hands well? Also, how wide does he view your 4bet range is important. A lot of factors come into play here and if you don't know them you will never know what's the best play and I would simply state that both shoving and C/folding are equally good plays.

However, I would lean towards C/folding due to your history of how he played 99 in blind battle. If he's not 3betting 99 it usually simply means that his 3betting range is polarized between monsters and some random suited connectors/gappers etc. If that's true, then it is very possible that he never gets to the river this way with JJ, possibly not even QQ (highly doubt it, I mean QQ should be considered a monster by even the biggest nits) AND the "bluff" range of his 3bets pretty much smashed this board with 2pairs and straights. So that would easily narrow his range down to very little you beat and make C/folding easily the best play.

With that said, my assumptions are somewhat long-winded and likely not true. He might not even have a bluff range for example. But when 2 decisions are so close in-between it would be enough for me to choose C/folding over shoving.

And I agree that we should probably bet something committing on the turn so we wouldn't have an ugly river decision. + it looks bluffy. It seems like you're trying to represent a straight and he might think "He can't have the straight, he 4bet me pre !" and just stick it in.