i almost always just call it (i accept that its incorrect and a leak of mine), for metagame as much as anything else, although pot size is also very important, ie am i good 1 in X times here? for metagame though, if i see anyone fold to a couple of river checkraises i will be pulling plays on them all session. i actually dont find it happening to me too much though

i think when deciding whether to check it through (and sorry for being so basic here but its how i think about it) is to just give the vil or vils a hand range/s and how much the comparitive mistake will be...

lets say there are 2 fish, and a flush comes on the river.

and lets say the fish are identical and each has a 50% chance of having MP/TPBK or having a flush draw.

that means
a) 1 in 4 times they are both paying you off
b) 1 in 2 times one is checkraising
c) 1 in 4 times both are checkraising

so when you bet with the intention of calling 1 back but not 2:

you win 2 once, lose 2 twice and lose 1 once for an overall ev of -3BB... so it would be better to check it through

of course in game its never this simple and most rivers should be value bet but thats just a basic way of thinking about it.