The weight thing Is mainly down to lighter modern kit ,unles you go really high end with carbon the steel frame will be a pound or 2 heavier at worst .Its fairly easy to get even 531 sub 20 pound with good kit on .Which is significantly lighter than mine is currently
Yup reckon this is true, though it can get expensive quickly and there may be limits. I found most of the weight to be in the components on mine (BB and cranks for example will likely weigh a tonne if they are original.) Then there’s the wheels. Then there are things like seat post (which might be some weird old standard diameter and really limit choice of lighter replacement) and saddle. Then there’s quill stem and bars.
I did work out that I could get my old 531 well under 20 lbs, though it would have cost me a few hundred quid to do so (wheelset, chainset and BB, etc.)
Oh and depending on the frame you may need to spread it to take a modern rear wheel. Not really a problem but you may need to do some hanger bending to get indexing on the shifting working properly.