Here are my 2 cents. I think checking our sets only makes sense when villain is likely to bet when checked to and the majority of turn cards don't hurt us. Also only topset that has a hard time getting called by worse is a check in this spot imo. When the board is dynamic, so draws could change the value of our holdings, checking sets seems like a bad idea. Better to get value while we're ahead. Let's say we have 99 on 952 rainbow. I would not bet this and let opponent bet his double backdoors, gutshots, 5x and some random shit that I see often at the lower stakes.
I also play micro-low stakes and for sure opponents are call happy so i think we can expand our value range and bet more light for value and put more of our draws in our checking range because none is going to notice and exploit that.

Hi. Thanks for the question. So firstly I want to touch on the micro stakes aspect. In one of the foundation videos I talk about GTO vs exploitative play and what I explained was that we should always try to learn and study GTO but play to exploit as much as possible. Micro stakes is where this is true the most! So at these stakes I don't think it is hugely important to be balancing your range in these spots. Instead I would be focusing more on what specific leaks I think my opponent has and how I can best exploit that using different lines and betsizes. However, against a lot of these players checking sets OOP especially top sets will be the right play. You allude to a lot of the players not folding when they connect with the board but when you have top set you take away a huge portion of our opponents range that will continue. Allowing them either a free card to connect a bit harder or to bluff us would seem fine to me on dry boards. On wet boards obviously we want to push our value since we will get called or raised at a much higher rate.

When it comes to the theory side checking sets especially top sets makes sense for a few reasons. The first one I spoke about above is that we just block so much of our opponents continuing range that often the ev of check is higher that the ev of bet. This is because our opponent will have so few hands that can go 3 streets against us but when we check we allow them to bluff and allow them to hit a second best hand a % of the time too. Secondly as opposed to when we are in position we don't necessarily lose a street of value by checking. If you are IP and X back you finish that street. But when you X OOP your opponent will still bet a % of the time. Lastly when we play OOP we play at a disadvantage and in most spots will have a high checking frequency. In any spot where you have to X at a high frequency you need (theoretically) to protect that range by including both hands to X/R and to X call. Otherwise your opponent can just put tonnes of pressure on your checking range. Sets work pretty well in the checking part of our range as they don't need much protection. Say on the 952 flop Fredje used. 99 and even some 55 can work well as an X because:
1) They need no protection
2) They block portions of your opponents continuing range
3) We will have to X this flop quite often so need to protect our range

Now take a hand like A9 or TT on the same flop. These hands
1) Need protection - Pretty happy with TT to either get called by Ax but don't mind if we fold out the 3 outs either.
2) Either don't block or only block a smaller amount of our opponents continuing range so are good for getting value.

So to sum it up there are a few things which make us decide whether to X or not. Note that its not always X/R either. Perfectly fine on dry boards to X call with sets too! Here they are:

1) Do we have a large X range on this flop - if so we need hands in there to protect the range
2) If we do need hands to protect the range we want to choose the best ones that don't mind giving a free card. So again on the 952 this would be sets, some KK and a lot of AA
3) Do we block a lot of our opponents continuing range - if so checking can often be more profitable than betting by allowing our opponent to catch up or bluff. with hands that would fold to a bet
4) Is the board wet or dry - we slowplay a lot less on wet boards as the value of betting sets etc goes up because there are more hands that will continue vs a bet
5) Finally there's the exploitative part. If our opponent bluffs v weakness a lot - exploit that by checking and just calling and allowing them to barrel off. You won't lose value against their good hands as they'll be betting them too. If they call too much go for the bet bet bet line. Always be thinking about getting the max value in this spot vs this opponent.

Hope this has cleared it up a bit for you.

i hope you don't mind me leaving this here, i was going to make a post but i think it will fit in well. i was going over a range for 4s 5s 6c being the OOP UTG v MP flat call. and i thought this looks like a good spot to check at a very high freq, if not always in theory and have a lot of x/r and x/c. A fair chunk of our range has missed this board, but some has hit very hard.. i can see some hands here that want to bet as well so i am not so sure.