Turntable weight affects speed

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

Belt drive players are not designed for extra weight on them.  Oh, they will handle 200 gm records just fine, I mean extra weight.  Something to be said about record camps, too.  If you are seeking smoothness, fine.  For one who wants any "jump factor" forget it.

Try the "Origin Live Gravity One".....You will be amazed at the improvement in all aspects of the sound quality in particular soundstage and instrument separation as well base definition. Just my 2 cents and I do have heavy weights too so I can actually compare!

To add more context to the discussion, the OP’s platter weighs 4kg and the record weight is 291g - a 7.3% increase in mass which is positioned right over the axis of rotation.  I highly doubt that very slight increase in rotation inertia is causing the ac motor falling out of synchronous speed. I would look at lubrication and belt wear as the potential cause.