Hmmm. An interesting problem. Is there any sign of mildew on the tent? Was it packed tightly for a long period of time? It could be that some combination of moisture/warmth/tight packing has caused the polyurethane coating on the fly to deteriorate a little and become semi-liquid, and its now gluing itself together. It is my understanding that this was not uncommon in older tentsthose made a decade or more ago. If its a very uniform stickiness, this could be what happened.
Black Diamond Lighthouse
It could also be something else, something environmental when you last used it. So try this: Get a big bucket or plastic tub, fill it with warm water and a little Dawn detergent, and sluice the fly around in that for a while. Then rinse it thoroughly and air-dry out of the sun. Maybe some tree residue or something is causing it to stick.
If that doesnt work, well, you have a problem. Depending on the age of the tent, it could be possible for you to order a fly replacement from the manufacturer.
Otherwise, its probably time to buy a new tent. Sierra Designs Meteor Light ($239; sierradesigns.com) is a classic two-person backpacking tent really a great performer. I also like Marmots Aeolos 2P ($335; marmot.com), which has two doors and two vestibules for easy in-out and good gear storage. For something a little different, Black Diamonds Lighthouse ($379; bdel.com) uses a highly water-resistant fabric with Nextecs Epic treatment so that only one fabric layer is necessary. Ive been using a Lighthouse this summer and like it a lot.
I always recommend packing tents loosely in a breathable sacka cotton pillowcase works greatand most tent makers now include breathable sacks as well. It helps ensure the maximum lifespan of the tent.