Not weight by itself, setup/scram time in general is affected too by weight and design...Hmm - Weight? In an era of easily available tractors should not be a factor.
The M114 should use standard NATO ammo. I suspect it was the bother of having a (small) battery of unique weapons ... maybe no spare parts for them? Antiquated sights? Lack of manpower to man such guns? Like you said - age - worn? Poor condition?
Used up barrels needing replacement/relining - either now or after a meagre few hundred shots?
I can think of many reasons - and I'm no military person - but weight should be Least Concern
And in such a war minutes of setup time make the difference between life and death of the crew, and the safe-ish window to get in, shoot and get out gets smaller the closer one has to get to the frontline, which with older guns like M114 is compounded by their limited range compared to modern guns.
Ideally Ukraine would prefer self-propelled artillery alone, but it's not available, still, even towed guns with better mobility like M777 and various 105's take much more losses than SPGs.