Actually, let's talk about ranges. But let's take the villain's perspective.

He's playing $5.7. Flop pot is $0.40 and he has $5.6 behind. You lead into 3 other players and he raises to $1. What does he think you have when you lead since pre-flop you can have literally ATC.

First, he's discounting the premium pocket pairs and kings. Of course you might have a lesser king but presumably you'd have raised to isolate with AK and KQ. You could bet there with any two clubs any 5 and any pocket pair 66-QQ (though TT+ will be discounted also) - and of course any king. In your range there is 50 or so hand combinations of flush draws, 3 combinations of 55, 24 combinations of 66-99, 80 or so combinations of Kx and 144 or so combinations of 5x. Maybe 18 combinations of 22-44. Almost certainly he'll underestimate the number of Kx hands in your range. The board is paired and that must necessarily mean fewer Kx hands in your range - what he's most likely forgetting is that even K2o is completely in your range with the pre-flop check from the BB.

What is he trying to accomplish with his bet? If he's holding the hands you're scared of - 55, AK, KQ, KJ - and he bets... what exactly does he think he's accomplishing? He'll have to assume a lot of folds. Maybe he thinks you would call on a flush draw, but the maths for a flush draw aren't good for you. You'd be calling $0.7 that needs $2.8 or so to breakeven and there would be about $1.4 in the pot already - so you'd need to win on average an additional $1.4 and the villain only has $4.6 behind. If you were on a flush draw calling his raise isn't such a hot prospect because his short stack hurts your implied odds. I think it's somewhat likely that the hands we are most worried about are most likely to actually call the flop rather than raise it. I think the hands most likely to raise are the flush draws and maybe the weaker kings.

I'm not saying he'd be wrong to raise 55, AK, KQ, KJ and price out flush draws etc, but we know little about him and the only thing we generally try to get out of someone being short is that he's probably not that good. And not that good can mean many things including an aversion to betting hard with big hands (like AA preflop) because you just get folds and don't get paid off.

The most interesting part of this post is that it made me realize that when there are two cards to a flush on the board and I don't have one there are exactly 55 possible hand combinations of flush draws if the opponent can be playing ATC. It's always tempting to be paranoid about flush draws, but if one of the flush cards is a blocker to the more likely part of the opponent hand range and the hand range is not impossibly wide, flush draws can actually be quite unlikely.

Edited section - ! factorial notation uses multiplication and I wanted to say something using summation and got the wrong symbol. Since the summation symbol isn't exactly what I'm looking for I'm just editing to remove any ! symbols.
The 55 is basically 10+9+8+...+1. The logic goes - in the absence of known cards the total number of flushy starting hands is 12+11+...+1 (78) because it's Axs (12 combos) + Kxs (excluding AKs - 11 combos) .... + 4xs ( 2 combos 43s and 42s) + 32s (1 combo). Given that two of the cards are "known" or "dead" (visible on the board) we can see in the example where an ace is not on board that Axs is now 10 hand combos as AKs and A5s (given the hand example in this thread) are no longer possible - from this it's easy to deduce that the number of hand combos must be 10+9+...+1.
End edit

It's both interesting with wide and narrow ranges. In this example I said that hero would lead with 5x and came up with 144 combos of that. (By the way 12 card values other than 5, 4 suits, 3 fives: 12*4*3=144) When I compare 144 hand combinations for a simple bottom pair hand with the 55 hand combinations of flush draws it just dawned on me how small a proportion of a hand range a flush draw can be - and this is as wide as it gets. It's impossible to have more hand combinations of flush draws than 55 (on the flop - with back door draws becoming flush draws on the turn there can be 110 obviously).

While 55 hand combinations may seem a non-trivial amount any range narrowing hits flush combinations hard. Let's say it's not a BB check but someone who plays all suited connectors (32-KQ 11 combos), suited aces (12 combos) and suited broadways (3 combos KJ, KT, QT). That's 26 hand combinations. No small amount you say - let's put K and 6 on the board and we're down to 19. And if we put both A and K on board we are down to 11. A range of QQ-JJ alone is 12 combos (with no Q or J on board).