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

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.  

Hope the responses take a load off your mind. Like someone else said, it’s not the motor but the bearing that might be negatively affected over time. And of course it depends on how much weight. I was surprised at some of the conservative responses, because some guys talk about weights up to 1 kg (2.2 lbs) with aplomb. I think of it in relation to the weight of the platter that the bearing was designed to support. If the platter weighs 10 lbs (4-5 kg), then a 250g weight will probably do no harm. Or even a bit more. And clamps are good; I use the SOTA reflex.

I think your Denon  motor/bearing, like my JVC TT81 is substantial enough to handle extra weight. I use the Audio Technica AT618a.

The Luxman and others use a ’reduced weight’ motor/bearing design, and you would not want much weight, these rubber holders for reel to reel players also fit TT spindles

new rubber holder, press on spindle, $10

I own an AT618A that I purchased in Tokyo on one of our visits.  (Sometimes I just buy stuff I don't really need only because I am there and it costs less.) It weighs 600g, or more than a pound. I use it only on my SP10 Mk3, which has a 21 lb platter, on the basis that the record weight is only about 5% of the platter weight for which the bearing was designed and therefore should not hurt the bearing. But I certainly would not say the 618A is too heavy for a TT81, etc. I use a 250g weight on my TT101. The AT618A really does seem to get more out of the SP10 Mk3 than the SOTA reflex clamp, for example. That is a purely subjective off the cuff judgement. I do like it.

I just weighed the screw-on clamp from one of the SMEs, 355g (12.5oz). A tiny fraction of the weight of the platter (which I can't weigh: it swamps kitchen scales, bathroom scales are inaccurate and I no longer own a set of baby scales!)