Will a record weight harm the motor in a direct drive turntable?

The answer depends upon which particular direct drive turntable is being considered.

The Two Links are showing that the 59L will benefit from a Savvy Individual looking at it and returning it to its optimised operation.

It does seem there is no useful lubrication witnessed and a speed regulation component will have moved and have caused Speed Stability Issues.

Add to this a Platter Spindle Bearing that is rotating off axis and this will cause issues with Speed Fluctuation for two reasons.    

A Platter Spindle that is rotating off axis, in a Dry Environment id undergone a latge amount of rotations, is also highly likely to be wearing down metal parts that are Sacrificial and Softer by design. Particulate produced through wear of the softer metals and has the particulate present in a dry environment is going to cause an unwanted accelerated wear at other important interfaces. Noise being generated through grinding, which is being transferred to the Stylus is inevitable as a working condition.

Adding Weight will be a method that improves the grinding and is a further accelerant for unwanted wear at critical interfaces occurring.

Adding weight to a Serviced Platter Spindle Bearing Housing that has adequate Lubricant, as well as a Platter Spindle the has a True Axis Rotation, is unlikely to cause any issues. There is also a better safeguard to be adopted, which is for the Bearing Housing to be periodically investigated/serviced/ with any Sacrificial Parts at a critical interface that is showing signs of wear having the part exchanged as part of the service.     

https://www.vinylengine.com/turntable_forum/viewtopic.php?t=137671

https://www.diyaudio.com/community/threads/denon-dp-59l-speed-control.423457/

On my Yamaha PX-2 direct drive, I am using a VEM Record Clamp which is not very heavy but has Dynamic Damping.  Seems to work great.  

@bobsdevices Yamaha PX-2 DD, I so wish I chose this model over the TTS 8000 when I was collecting Vintage DD TT's to have fun with.

The GT's had crept in Value and were quite a few £'s more than other selections made. Mind you they would have been a great investment, as typically they are the best part of 200% appreciated in today's money, where as my TT's are still found at similar monies as when acquired by myself.   

How much weight exactly are you wanting to add?

I have a Kenwood KP-9010 and Kenwood sold quite a few accessories one could purchase to enhance the performance of these DD tables.

All the accessories that were sold for the L07 Kenwood's would work on the KP-9010, KP-1100 and maybe others.

Pretty sure the DD motor on your 59L is a high torque model. I'm not gonna say "no problems" as I have no idea how much weight you're talking about....

Has your table been restored? Caps, resistors, brought back to spec?

If not, and you're running all original electronic parts inside the TT I'd probably not try at all. If you're thinking of adding weight I'd have the TT internals restored/upgraded first.

Aldo