weight scale

so when a rock generaly weighs at 0.65, but occasionaly measures .066 while calming down, and will read more often .066 than .064, i should assume its true weight is closer to .0655 or 0.654, rather than .0653,..... correct? ( it cant weigh .0656 or otherwise it would be at 0.51ct )

I will assume your assumption is correct.

Your assumptions are quite good.

Balances take a while to settle. They are better if given a few test weighings to do prior to the real one. They call that exercising the balance.
Has to be in a very stable environment, no air flow  or A/C on.
Generally they will go 0.062, 0.064, 0.065, 0.066, 0.065, 0.064, 0.065. Then wait for 10 seconds or more, it may or may not click up to 0.066.
It it reaches 0.066 momentarily while settling it is probably a bit less that 0.066.
I used to calibrate balances.

Good luck