The flight controls of most modern fighters auto-trim to 1.0 g. However, the pilot will still be able to tweak that datum using the stick top trimmer, in case the nul setting is off by a small amount (design imperfections / system errors etc).
Aircraft like the F-16 will pitch-up when in a climb or dive because the system will seek to achieve 1.0 g in all flight regimes (i.e. when in a 45 deg dive, the normal g should be 0.7). In more modern aircraft like Typhoon, the flight control laws are designed to compensate for these changes - so it's even easier to fly (and employ weapons).