Like lots of things it depends. Conventional wisdom is that we bet for value or bet as a
bluff, that's on every street including the flop. If you hit the flop hard then bet is a good rule of thumb.
If you miss the flop and are considering a bluff then how does the flop suit your range vs. your opponents range is something important to think about.
Example: If you raise first in from the cutoff and the big blind calls, a bigger percentage of your range is typically going to be occupied by big broadway cards. Why? It's because they should in theory be re-raising (3 betting) many of the bigger
hands themselves. Things like AA down to TT, AK, AQs, AQo KQs, JTs. The fact that they didn't 3 bet should indicate to you that they are less likely to hold these kinds of hands. So if a flop comes with two cards 10 or higher it can be a good spot to cbet a little more often a lot of the time. You could still hold all these big hands following your raise, they don't know if you do or do not.
The kind of hand that the big blind should call instead of 3 betting versus a cutoff raise is more of the smaller pairs so a flop with a couple of big cards is bad for that. They should be calling with many smaller suited Aces, Kings Queens and Jacks too, hands like J 6 suited, Q 8 suited so on that flop with 2 big cards you are more likely to have 2 pair, and even if they hit middle pair they don't have such a great kicker and may fold to a cbet. They should be calling with many lower suited connectors or two gappers too so a flop with 2 high cards looks bad for them a lot of the time (slightly less so if there's a flush draw out there).
In the same situation, if the flop were to come something like 8c 7c 4d and the big blind called it's a worse flop for you cbet on. They didn't 3bet so are a little more likely to hold something that made a straight, a set with a lower pocket pair, 2 pair or landed a big combo draw than if they did 3bet. From the cutoff you can still have all the same kinds of hands too, it's just that the likelihood of either of you having something like that is much more even.
Now here's the thing, the opponent might not know the kind of hands they should be 3 betting with and may call too often compared to theory. If they're doing that, they may have more of the big hands themselves when they just call your raise. They may also understand the theory but decide to play unconventionally for whatever reason, perhaps to throw you off guard. It's very important to see what kinds of hands they 3bet with and what kind of hands they just call.
In general, is a particular opponent folding too often to cbets? Make cbets slightly more often as an exploit.
Is a particular opponent tricky, check-raising you more often? Be a little more careful, check back more often.
When it comes to sizing, smaller cbets can sometimes see an opponent defend more often, larger ones can attract more folds but isolate us against a stonger part of their range should they call but again that's dependent on the kind of player they are.
The size of your cbets can also say something about you. If you only cbet 33% of the pot when you don't have much but make it 75% when you're strong that will be easy to spot, the same if you do it the other way around. That's why some players will pick one size for all cbets. If you are going to change the cbet sizing then it's better to try and do it in a slightly more unpredicatble way.