This is one of my bigger leaks, and I still am not sure how to protect against it. Often times, I will bet two or three streets with position into someone with a set. I will have a strong hand like two pair, an over pair, or TPTK. After they C\C my flop c-bet, I usually bet the turn as well.

My logic is that 1) Often times, players will peel one street with a weak holding like middle pair, 2) I do not want to induce them to bet on the river without knowing if their hand is a bluff or a value, and 3) I will frequently get called with top pair weak kicker, or a middle pocket pair.

This might be a stupid question, and maybe I am missing something obvious (like checking back the turn to limit pot size), but is there a way to protect against a set that doesn't leave a ton of money on the table and isn't exploitable?

Just look at villains range to call. If there is enough worse to get value from bet, if there isnt checking and bluff catching becomes a better play. You cant start seeing sets everywhere, obviously know your opponents, but eventually you are going to run into sets. phil galfond once said if your are never value betting and getting called by better you are not value betting think enough.

You don't "protect" against a set, because you can't make villain fold a monster hand.
What you can do is work out how much of an opponent's range is beating you when he check-calls two streets, and then decide whether your hand is strong enough to triple-barrel for value. If you had TPTK for example, and knew that more than half of villain's turn-calling range was 2pr+, then you'd check back the river. Your turn bet might "protect" against draws (including worse pairs that could river 2pr/trips), because it sometimes makes them fold. It won't 'protect' you from hands that are already ahead.

To put it another way, you might bet the turn for a mixture of value and protection (some worse hands can call and some hands with decent equity might fold), but you won't also bet the river, because it's mostly only better hands will call.

Another line might be to check back the turn in order to keep villain's range wide. It's actually good for you if he bluffs the river, because you snap-call and beat his bluffs. If you bet the turn, he'll often fold hands that would have bluffed the river.
You're gonna lose to a set no matter what, so think about how to get money from the weaker hands in villain's range.

No there isn't a way to protect against sets if you have any reasonable barrel frequency. If you barrel wide they call wide so you need to vbet thin so it sucks when you run into the top of their range. It's better portrayed when you 3bet SB v BTN 100bb deep effective and you bet, bet jam on a K52 89 board with AK and villain shows up with set. You can't do anything. That's why it matters how much you make it preflop because good players can make better reads when SPR is high. If you beat 50%+ of his range that he calls with you need to jam.

It's like blaming yourself for bet, bet, bet/calling a river shove w K high flush and being shown the A high flush. It's like whatever. It has to happen. You will lose money a lot of the time even if you play top notch over the top ****ing incredibly perfect.

Your winrate isn't dominantly a function of set vs overpairs. It's dominantly a function of every small piece of EV you pick up here and there by making correct bets/raises, calls and folds.

Not checking because you don't want to induce a bet is insane. There is no reason to keep betting just to prevent them betting the river. You want them to be bluffing if they have a worse hand.

Thanks. I think your and Arty's comments are making me see that not checking the turn if I am check called on the flop by a strong player is probably one of my mistakes. My goal had been to simplify my river decisions, but I think I am not really gaining anything, and, if anything, making for a difficult decision on the river with a bigger pot.