I'm not sure what the weight criteria others use are, but for me I take the listed weight (26.73 grams), figure mint variance at +-0.5% or 26.59 if on the low side of tolerance (this is my guess - I've never seen a listing of actual mint tolerances for weight) and I use a wear tolerance of another 1% - so a worn Peace or Morgan weighing less than 26.3 grams would (barring other criteria) make me look twice extra hard.
I recently bought a fake British
Trade dollar (the real ones weigh 26.9568 grams per Krause) and it weighed around 25 grams (around 9.25% less than the listed weight) - but the design was really close to a real one (which is why I bought it - as a comparison piece against real ones).
For my comfort level I would pass on anything that was less than 26.3 grams (as mentioned above) and look critically at anything that came in around this level.
Maybe someone else will chime in with better knowledge, but I really doubt a worn silver dollar looses more than a gram. Bear in mind that I wouldn't buy anything less than F-EF (I like to see the designs), so I don't look at a lot of AG-G silver dollars.
At the end of the day, if you feel anything about a coin makes you feel funny, I recommend passing on it. There are lots of coins out there, so it pays to pass on any one (and at least build up your knowledge till you no longer feel uncomfortable about what you are considering buying).
Good luck and use that scale!