My turntable (Technics) makes it very easy to adjust VTA to compensate for differences in thickness, to make sure tonal balance affected by VTA remains fairly constant.
Concerning the variety of record weights (e.g., 140g, 180g, 200g), different weights have different resonant frequencies, but a record grip like the KABUSA dampens the record's resonant frequency and minimizes that difference. I use the KABUSA and it helps put a Dynaflex and a Classic in the same sonic ballpark.
But after all that, there is--to these ears--an audible difference in sound quality of the 200g Classics I have. They reveal superior recovery of low level detail more like the master tape itself. I think these differences are attributable to:
1) Classic's tendency to use the original 2-track master rather than a copy (1 less generation of deterioration)
2) Bernie Grundman doing the mastering
3) Bernie's tube-driven cutter
I suspect the tube-driven cutter particularly enhances the low level resolution, as low amplitude linearity is probably the strongest suit of tube-driven electronics.
I just got two wonderful 200g Classics this week, and they stun me every time I put one on for their comprehensive retrieval of everything that went on in the studio. I have a mid-priced system, certainly nothing expensive, but with the Classics (a Holly Cole and a Norah Jones), I don't just hear the music, I hear how they made the music, right down to being able to visualize how the vocalists are shaping their mouths to sing the notes.