Unless instruments are particularly valuable/collectable, I see very little point in keeping them if they are not comfortable to play due to weight issues.
So, unless you are expecting your ailing back to improve, sell the heavyweights.
I can recall in my younger days always striving for "that sound", spending time and dosh on preamps, active basses, different amps etc. It all seems to have come right for me now with passive precisions and the eq on my amp, which is a Genz