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

In general Making a motor work harder can only shorten its life. 

It’s never a positive thing in that regard for sure.  

Each case is unique. The benefits need to outweigh the disadvantages.  Unless a table is explicitly designed and guaranteed to handle a certain amount of increased load beyond normal I would always proceed with caution. 
 

On the positive side,  adding weight near the center spindle is less problematic than if added further from center. 
 

Heavy center weight and outer ring is my ritual. I never do without on my VPI Classic. I remember emailing someone at pro-ject about using a heavy center weight on their debut TT and he said NO, not can do, motor won't handle it. Always reference to manufacturer. If heavy center weight is not an option, simply use a clamp. I do that on my second TT, Pioneer PLX-1000.

I would recommend the “Serene Stabiliser” from Stack Audio. It will provide what you’re looking for and minimal weight. Much better than a typical clamp. 

+1 @g4mobile 

Aside from trying to reduce the effects of a warp, record weights and outer rings are attempts to change the sound to tune it to one's preference.  It the weight more effectively couples the record to the platter/mat such that internal vibrations in the record itself are transferred more effectively to the platter and better damped (the usual intention of such weights) that MAY improve the sound, or it may make it subjectively worse; it really depends on what the rest of the system sounds like and what you are looking for in the sound.

I have Basis Debut table with a vacuum clamping system.  This is pretty much the ultimate way to couple a record to the platter to dissipate vibration in the vinyl that will feed back to the stylus.  If you place the stylus down on a record that is not spinning at tap the record surface with the back of a pen near the stylus, you can barely hear sound coming from the speakers.  If you do that with other tables you will hear much more of that vibrational energy being fed to the cartridge.  So, this is definitely a good thing?  Not necessarily.  Some people find this degree of damping to be excessive and subjectively "dead" sounding.  It really is system and personal taste dependent.  I've played my table with the vacuum off, and sometimes, I prefer the sound that way.