Weights in general are the simple, cheap, and not very effective way of clamping a record. Also because of the way they work they have to be heavy. A reflex clamp by contrast grips and pulls against the spindle and so can clamp much more tightly without the need for mass.
Also record weights don't really do much to flatten a record.
Either way, the one key element missing from most designs is a washer or shim that fits over the spindle and is just thick enough to sit slightly higher than the platter surface. The center of the platter is recessed to allow space for the center label area of the record which is thicker. So with many designs the more the record is clamped down the deeper it goes into this recess and the more it forces the outside of the record to cup up. Hard to believe, exact opposite of what you want, but a lot of them do this. Try a few and see.
A properly designed reflex clamp with washer on the other hand will press the record down onto the platter across the whole surface clear out to the edge. Even somewhat warped records are pressed flat. Record weights don't even come close.