Indeed...building core strength would be the more sensible option, actually increasing weight by increasing lean muscle mass over body fat in the core areas.
The reason I have a bad back is 20+ years filling shelves in a supermarket and it's been 16+ years since I took a tea break or stopped for lunch. I've always treated it like going to the gym, and while my bad habits have finally caught up with my spine (triggered by a particularly hard build up to Easter trading in these budget-squeezed times), I eat pretty healthily and take core fitness very seriously. It is, after all, the tool I need for my work! So I'm lean, healthy, and strong in a 'normal' sense.
Except for a few of my disks.

But I did gently build up my crunch capability when the sciatica started, hoping to build up my core strength, and 300+ at a row is now not a problem. But at 10 stone I am definitely flabbier around the waist than I prefer to be, and if I'm much more comfortable and feel "springier" and healthier down at 9'7. I just lack the willpower to avoid biscuits and stay there for long, and now I've hit 50 there are definite signs that my metabolism is trying to slow down.
Either that or I'm just knackered.
Anyway, going back to the OP's issue, ultimately weight is all about what we as individuals are comfortable with. I had chronic asthma for the first 20 years of my life, so was a bit chubby and very unfit for all my youth. But as soon as the asthma came under control I was, and still am,
so happy to be healthy that I swore I'd never let myself get fat or unfit. So far I've managed to keep that promise to myself. But not everyone is going to be fortunate enough to have such a powerful motivator, and food is
great entertainment.
I shall now go off and be entertained by half a packet of Jaffa Cakes. Then the other half, probably. I'll no doubt end up with diabetes
and a bad back. :->