I'm no anatomist, but all that should be happening (from a physical standpoint) ..would be that its intestines, gonad, etc would settle near the fish's stomach/anus area. Nothing critical is getting crushed.
From a mental standpoint, the fish can't think....it's not thinking why is the human holding me or what's he going to do next. I would think that the fish's instinct is fear, whether or not your unhooking it to release it OR weighing for the few seconds that it may take.
For me personally, this low addition (weighing process) to the already experienced stress of being hooked and dragged to shore would not deter me from weighing something that I felt deserved the respect of being weighed. Yes, there is some inner-ego in yearning to know if this particular one is your personal best, but there's also respect being shown to the fish...as not all are worthy of seeing the scale.
Who knows, maybe it even makes the bigger fish feel better by stretching the spine....maybe it forces some new blood into some old crevices.....always seems to help the old lady....LOL
There is some truth in there somewhere...for those who choose to seek it.