Heavy Vinyl

I did a search and see that this hasn't been discussed in quite a while. Heavy vinyl is touted as being better for sound quality. I wonder about this. For a start, it is more susceptible to warps and particularly those short duration warps that really give the cartridge a hard time. Second, in my own listening across a fairly extensive record collection, I'm not hearing any particular sonic revelations from heavier records. I'm more inclined to believe that the critical factor is the quality of the vinyl  and the stampers used rather than the thickness of it. Other thoughts?