Record clamp/weight and turntable speed


Hey all. So today I thought for the first time if having a substantial weight or clamp on the spindle affects the platter rotation speed. It doesn't for me, as far as I can tell, but if not, why would that be so?
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I have a slight twist on the OP's question, in that I have a 70's era Thorens 145 belt-drive turntable that I have introduced a center weight to.  As was pointed out, this weight does not affect the platter speed at all, it just takes a slight moment longer to come up to speed, so, no issues there.

However, on these Thorens tables the center spindle is not overly long, so, with anything at all other than the original rubber mat (which is quite thin) elevates the record to the point where there is hardly enough spindle to engage the hole in the middle of the weight (the weight I have also has a slight taper on the underside I suppose to help someone guide it onto a spindle).

I try to get it centered which helps most of the time but there are times when the weight is rotating a bit off-center.  It does not affect the sound at all, but, just curious if there is any other thing it might be doing?  

Also, some may be worried about VTA, but, we are talking a slight slight elevation here, not enough to change the VTA requirement.  Even with the factory mat on the table the spindle barely clears the center piece on that table (which is also the 45 adapter if turned over).  

Thanks for any thoughts or comments.
I wouldn't worry one second about the slightly off-center weight, but if the aftermarket mat is thicker than the original, and if you have set VTA while using the OEM mat, then the VTA will have been altered by a tiny amount.  It's up to you to decide if that has affected SQ or tonal balance.  Probably not, is my guess.  If you are using a cartridge with a line contour stylus, which is very sensitive to VTA, listen carefully.
Don't know where you've been for the past 400 years, dover, but "proper" never has meant "reflex" not in any dictionary I have ever seen. But I tell you what, since you want to argue so much, find me the clamp you think is "proper" as described above. One that clamps the record down so flat and secure it has to be lifted by the edges after playing. You find that one for me, post a link like I did for mine. That way I can explain in detail what you missed and why it is, compared to mine, not a proper record clamp.
VPI.  Screw down with threaded spindle.  Washer between the platter and the record.  Mine was a TNT 3, (25+ YO design). I had to lift the edges to release the record.

I still miss that table, sorry I sold it.
@lewm thank you for your response.  As for the VTA, the current cartridge (Grado Prestige Gold) was set up by a shop with the factory mat plus a felt (I think it is) 70's anti-static mat and the two of them together is about the same as the replacement cork mat I just bought.  So, I believe it is very close if not the same height off the platter as it was before.  I just introduced this weight though and had no clue prior that there would not be enough spindle still sticking up to catch the hole in the weight. I think I will not worry about it for now and continue to listen to a number of my very favorite go-to albums that I have heard so many times that if the SQ is off, I will certainly know it.
@xaak - My Herbie's Mat has a rubber washer between the platter and record. What does that do for the physics of clamping?