Barber dimes (and Mercury dimes and silver Roosevelt dimes) were all supposed to weigh 2.5 grams as minted, with some small variation above or below that. A heavily-worn Barber dime like yours can easily weigh 20% less than normal, or under 2 grams. If if really weighed 3/10 what the other dime weighed, though, something would be wrong. If a dime were worn down that much, you wouldn't be able to see any detail on it, I'd think.
Ok so I'm confused is my dime good or no it did weigh 2.1 and the other weighed 2.4 but as chunks missing and I even reweighed it to be sure.