And I check-raise for value, not for fold equity. Although you'll make some cents if he folds the A of spades, most of the time I'm still rooting for him to call.
I think fold equity does have something going for it, even when you're a favourite. You have to look at how much
of a favourite you are. In this case my opponent had 10♣10♦
and although I'm technically a favourite, it's as close as you can get: 50.10% vs 49.90%. So if he calls, my long term net gain is 0.1% of the pot with us all-in. If he folds, my long term gain is the whole $4.10 that's in the pot already, which, for comparison, is about 11% of the pot above.
So in the case above I would need to be 61% to win the pot to prefer a call over a fold. You only get this kind of odds versus an overpair with a pair + straight flush draw, e.g. if the flop here were 4♠5♠7♦
Obviously it depends on the pot size - the bigger the pot, the more you prefer the fold. And... I'm making this up, so feel free to point out any flaws in my logic.