How tight do you tighten a record clamp

Depends on design of the record clamp, not sure what do you mean, but i have only one Disc Stabilizer with chuck (lock) around the spindle. It's rare japanese Orsonic DS-250 It's impossible to damage anything with this stabilizer, also i think this stabilizer can be used on aty type of turntable from belt-drive to direct drive, self weight is only 250g, but with this chuck (lock) it's pretty easy to make any record absolutely flat on the platter without too much force. Also no harm for the bearing or not too much weight for the lightweight platter of the belt-drives. Beautifully designed unit by reputable Orsonic engineers. 

The other stabilizers i use are much higher weight and without chuck/lock for the spindle, but my turntables are Direct Drives. 

Don't use these:

https://en.wikipedia.org/wiki/Locking_pliers

just finger tight is fine.

My analog is a vpi  scout with grado sonata wellbourne tube phono

I tap lightly on the record with the back of my fingernails as I tighten the screw-down record clamp. The record will give off a hollow sound until the clamp hits the right level of pressure. Then it will sound solid as the record mates tightly against the platter.

When the record is properly mated to the platter, the soundstage and imaging come into focus and the upper midrange and treble is smoothed out, bass is solid.

I don’t know if your scout has a threaded spindle to fit a VPI record clamp rather than a weight.  I'm using an Aries Extended with a platter / spindle that is set up for a VPI screw-down clamp.

@g11657 Great question - I've always wondered.

I have an MMF-5 with felt mat and was always thinking I'd might pull the center down too much and make the disc concave. FWIW, I always just go finger tight to make it snub, not finger tight till I can't turn it anymore.

 I just bought a Herbies mat, but haven't received it yet. I'm thinking the platter mat will make a difference depending on how flexible it is.