Why am I damp?

What kind of sickness did you have? If you had a bad cold (or manflu)
Then you might of had a fever, that would soak anything.

Use less insulation? Open up your quilt some?

What kind of tarp shelter are you using with the quilt?

Night sweats can occur with some illness.

You mean home use? There is insensible and sensible body moisture/perspiration. The former is moisture vapor that your body releases, sort of like humid air, but you don't really notice and generally quilts pass it through pretty well. It's a vapor, not a liquid, but under the right conditions can condense into a liquid.

The latter is sweat–obvious, noticeable, liquid wet from the get go until it converts into vapor. Sounds like you were sweating under the quilt. Too much insulation, a fever contributing to higher body heat, and/or a combo. Not good to sweat under a quilt.

Yes, this is indoors at home. The thing is when I uses my sheet/fleece blanket/sheet combination the dampness is much less or not there at all. So maybe it is less insulation or more permeable than the quilt.

I'd sweat if I tried to sleep in a 3 season quit inside. It may just be that the quilt is warmer than it needs to be for indoors.The sheet, fleece may be suitable for 50 degrees while the quilt is made
for colder weather than you face indoors. Likewise if I tried to sleep in 40 degree weather in a fleece and 2 sheets I would probably freeze.

I once had an REI Sub-Kilo sleeping bag that made me horribly clammy at any temperature — and I wasn't even sick. It's the only sleeping bag I ever owned that made me feel that way, but other folks loved that model of bag and gave it great reviews. (I returned it.)

While I can't prove this, I think it was the inner fabric that reacted with my body chemistry to create the clammy-effect… haven't had another sleeping bag with that effect.