If your "card" is fatter than 1/4", it won't go through the auto sorter at the postal system. It will have to be hand cancelled and they charge more for that, regardless of weight.
I make up all my packages at the beginning of the year, and by the time the birthdays roll around, those cards are flatter, with the fabric squares having settled in and compressed somewhat. If I insert the fabric in 6 piles of 8, plus 2 more on top, my cards are always less than 1/4" thick. I use the 2 ounce letter stamps on them without problems.