Turntable weight affects speed

Hand spinning will get it up to speed. Once up to speed, the load on the belt/motor should be the same with or without the weight (physics). If it is different, then you have something dragging or a bad bearing that results in extra frictional force exacerbated by the weight.

I asked someone at pro-ject if I could use the same weight I use on my VPI Classic on the carbon TT and he said NO, too heavy for that TT. So, yes. Not every TT is built to handle those weights.

I have a clamp from, Mitchell (I think) that's made for Regas and it's a spindle grabber...on a Linn...works great and will keep the record on there in a strong windstorm. Seriously, you don't want your vinyl to blow off the table although I suppose you could simply close the window.

Since the record weight is positioned over the axis of rotation, the added mass does not substantially affect platter’s rotational inertia, therefore, your motor should have sufficient torque to start and maintain platter speed. 

@carlsbad2     "the load on the belt/motor should be the same with or without the weight" (INCORRECT physics). 

You are possibly thinking of Newton's Law of conservation of momentum.  But if the platter is spinning and you cut the power, it won't spin forever.  Ergo it takes power to keep it spinning.  How much power?  I clearly takes more power if the platter + record weight is heavier as the moment of inertia is greater.  Pace @testpilot , the point you make is correct but there will still be more inertia and this may be sufficient to prevent the motor on the Thorens keeping it moving at the same speed.

Yes, check out the motor, belt and clean and re-oil the bearing