I feel I have to put an opinion on this - & opinion it is, because there are too many factors influencing vinyl quality.
Attention to detail in the cut.
Will affect every pressing of any weight.
Attention to detail at the plant.
Do they run each stamper 100 times before cleaning & 1000 before replacing, or do they run 10,000 before cleaning & replace after 250,000 pressings?
A third, more cost-conscious alternative - do they run the heavy-weight audiophile pressing for only the first few copies of each stamper's life, then swap the process line to regular pressings?
Recycled vinyl content.
Every pressing leaves waste to be cut from the edges. In the old days when everything was on vinyl, there would also be old recycled over-pressings & even ex-jukebox rejects to add to that. Does your copy contain only virgin vinyl or mainly recycled swarf?
Weight is really just 'thickness', nothing more. They used a bigger glob when pressing the audiophile copy than the old HMV bargain bucket compilations.
Yes, it is more inherently stable, though if warped it will warp badly - but that may be down to transportation & storage and out of the hands of the pressing plant.
...but the weight itself is simply the end of a long line of areas where your expensive audiophile pressing received greater attention.
your expensive audiophile vinyl - you would hope - is prepared for you with high attention to detail in all the above factors.
I feel that is what makes the real difference, not just an extra 50g of plastic.
One last point…
Is heavier vinyl 'more durable' than lightweight.
Of course not!
It's exactly the same groove you have your stylus in, however much extra plastic is between you & the B-Side.
But that takes us back to how much ex-jukebox dust & other extraneous floor-sweepings are in your nice shiny black stuff.
Virgin vinyl lasts longer because the contaminants are lower. Dust doesn't wear at the same rate as vinyl, so it generates pops & clicks where each softer [or even harder] contaminant is passed over by the needle & changes the erosion rate of that portion of the groove..
I sometimes download dodgy flacs of albums I may buy
[shoot me, I'm not rich - if I don't like it I bin it, if I do like it I buy it]
I have just been listening to the audiophile vinyl (as FLAC 96k) of the last Bowie album, The Next Day… until I got so irritated by the sound quality I just went & bought it on AAC directly from iTunes - the difference is stunning...
…mainly because whoever uploaded the dodgy version had possibly the dullest record player I've heard in years. Missing high-mids & top, wooly low-mids, over-emphasised bass. The AAC is a whole polished glass window clearer than the dull, listless vinyl I'd been listening to.
So, word of warning - vinyl is not inherently better, if you don't have a player to match your expectations. Good turntables are really not cheap. They demand a whole lot better throughput than a couple of Burr-Browns & need more care & attention.
Of course, the downside to my knee-jerk reaction to buy an album I was testing to see if I liked it means I now bought an album I don't really like, just to see what it really sounded like :-(