I didnt bet the turn for pot control, I also wanted to keep the fish(original limper) in the pot as long as possible also.
I don't agree with this thinking to be honest.
First of all, you really shouldn't be worried about pot control at all in this spot. The flop has checked through, meaning there's only going to be two streets of betting max in this pot which is perfectly fine, and with top pair top kicker pretty ideal in my view. You should be worried about value betting, not pot control here.
Also, the reason you want to keep the fish in the pot is so he can pay you off, so I don't think there's much point keeping the fish in the pot if the price you have to pay is not betting a hand that is extremely likely to be best. Again, you should be worried about value betting in this spot rather than keeping the fish in.
So I would definitely lead the turn. There are a lot of worse hand you can call with so you should bet.
However, as played, I think this is really strange. It's a really weird line for Villain to take if he's bluffing, and all you've got is a bluff catcher really.
I would really expect the Villain to bet most of his air on this flop, even three way. I would also expect him to bet his top pair/overpair type hands and don't see any reason why he would take this type of line with TT-44. I would also expect him to give up on the hand if he has air and has decided to check this flop, because if he has air, why would he give up the most likely opportunity he has to win the hand only to try to win it later when someone else has shown an interest in the pot, although it is possible, though in my view a little unlikely.
The big questions for me are, what are his cbetting tendencies and what are his slowplaying tendencies. This flop is so bone dry that he may slowplay a set here. Two pairs are extremely unlikely to the point where I would completely disregard them. Regarding his cbetting tendencies, is he the type of player to bet all his middle pair hands on this type of flop? I think most people would bet 44-TT on this board, but maybe he's the type to check back for pot control or because he doesn't see much value in betting.
Just because I think he's likely to bet almost all of his air/top pair tye hands, I think his range for checking back is most likely JJ, 33, 22, and TT-44, depending on the player. While you may think his turn bet looks weak, he might be just making a small bet for value with the deck crushed. I think he can definitely bet 88-TT on the turn got value, but I don't think he would raise the river with them.
Basically, I think his range on the river is completely polarised. I don't expect TAG-fish to be mixing up their play by checking back top pair type hands. So when he raises on the river, he's either got a monster i.e. 22, 33, 77, JJ, A3 (which I'd expect him to bet on the flop so I don't think is likely) , or a complete bluff. Given that TAG fish generally don't bluff raise the river, I think you're probably beat a large amount of the time. But on the other hand you're line looks really weak. You're getting about 7/4 to pick off a bluff which I don't think is great, given that this guy is a tag fish and for him to be bluffing he has to a)check air on the flop which I don't think is likely and b) read your hand which he may not be even trying to do and c)realise that you're range can't stand up to a raise and then d) be able to pull the trigger on the river.
Given all that I think I would just fold, until I find out he is capable of bluff raising the river when his opponent is weak, or capable of checking back middling strength hands for balance.