Some of the comments above demonstrate a complete lack of understanding of clamps/weights. You have to look at the total picture, in particular what is under the record.
Example
Record weights do little to bond the record to the platter, so they presumably are not in the business of optimising resonance-damping through this interface.
Real answer is - That depends on what is under the record.
Some clamps/weights are designed with a slightly concave platter or platter mat and the downward force couples the record to the mat.
Examples here are
Goldmund clamp/mat - reflex clamp with concave mat
VPI Classic - screw clamp with concave platter
Most heavy weights will help couple the record to the platter if the platter is slightly concave
Some clamps/weights are designed to work with a washer under the record. These will have a peripheral edge that applies pressure to just inside the outside edge of the record label such that the clamp/weight when applied couples the record to the platter/mat.
Examples are -
Sota Reflex Clamp - uses a washer under the record.
Final Audio VSD17 - a 1.8kg weight with a peripheral edge that uses washers under the record.
When I look at most of the clamps or weights on offer, then, unless they are used in conjunction with a concave platter/mat or washer they will do very little or nothing. They might possibly help reduce any slippage of the record during play. If all they do is reduce "resonance or vibration" then a potato impaled on the spindle might be just as effective.
There are some caveats as as been pointed out above -
Use of a heavy weight with a suspended deck may impede the performance of the deck.
Use of a heavy weight may accelerate bearing wear if the bearing quality is poor or not designed for heavy mass.
Dont assume anything here, I have seen bearings on the some much vaunted TT's that are made out of junk metal. Check your oil after a few months - if its dirty, then your bearing is wearing out.
On the subject of mats one of the most ill informed reviews I read recently in an online magazine did a shoot off of mats on a Garrard where they compared leather, copper & carbon mats. Well anyone that has owned a Garrard should know that Garrard platters are slightly concave and unless you have had the platter top skimmed, then any hard mat is only supported at the outside edge and would most likely sound awful. No mention of this in the review. No wonder people in this hobby get led up the garden path.