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My catalog has a 5.6 oz 50/50 Gildan, and a 5.5 oz 100% cotton pre-shrunk Gildan. Aside from that, I sell the 6.1 oz 100% cotton pre-strunk. I do not particular like it's feel, but my customers love it, so there I goes. I do not do screen printing, just zigzag stitching. I like the 5.5 oz 100 % cotton Gildan, because it has a very similar feel to the 50/50 Best tee, which my customers no longer care for. The 50/50 Jerzees strink after 15 or 20 washings, which has been my experience, and therefore is the cause of anything Jerzees, except, when they have a color that nobody else has. I have no experience with anything 100% cotton Jerzees, and they may be an excellent product, but I am a Gildans man now.
This probably does not help you, but I thought I'd pass along my limited experience, anyhow.
Smith
The 5.6oz is suppose to represent the weight of a square yard of the fabric. So, the 5.6 should be thicker than the 5.3. But that's not always the case in the real world. Most of us would not be able to tell a 5.3 from a 5.6oz garment.
You should samples of both shirts and press your designs on them so you know for sure which one will serve you best.
I just ordered mine ( it says style g200 ultra cotton ) from blankapparel.com . No license required and S-XL was less than $2 each for all whites. the 2XL and bigger is more than a dollar more.