How to Travel Carry-on Only as Huge Dude?

Fiancée and I are going on a 12 day trip to Greece as a sort of field-trip for her high school students. As a result, we don't get to pick the airways--we're stuck with ITA airways which I've heard has astronomical prices for checked luggage.

We're bouncing around quite a bit and going on two cruises--I don't think I can get away with carry-on only as I'm 2-3XL, and have a CPAP. However, if you have tips, I'd love to hear them.