Do different pickups have different responses to different strings? Not in terms of gain or dynamic response, but just volume. I recently got a guitar that has a neck that plays very nicely, but the higher strings seem to get lost in chords, and even seem quieter when played alone.

This wouldn't be greatly affected by the body wood/body thickness, would it?

Anything I could try to alleviate this problem?
Maximum volume yields maximum goats.
if it has adjustable poles (screws/hex bolts) you can just raise those to get a louder sound out of them. if it is poles like a strat/tele single coil then you must adjust the pickup itself.
2002 PRS CE22
2013 G&L ASAT Deluxe
2009 Epiphone G-400 (SH-4)
Marshall JCM2000 DSL100
Krank 1980 Jr 20watt
Krank Rev 4x12 (eminence V12)
GFS Greenie/Digitech Bad Monkey
Morley Bad Horsie 2
MXR Smart Gate