I'd do nothing and se what happens. If they make you check overweight/oversize bags at the gate the fee is FAR less than your business class upgrade would be. In my experience I've regularly seen them check bags for size at Athens but never for weight. In any case, if the flights are quite full, gate agents roam the gate area choosing the largest bags and forcing people to check them anyway - for free. As has been said above, document the contents of your bag and see what happens. If you are pulled aside, the most it will cost you is about 30 Euro per bag and they probably won't even charge that if you are on a ComfortFlex ticket - just tell them you had a short connection and didn't have time to go to the desk.

Don't forget that the other benefit of the business class upgrade would be lounge access (on the outbound in ATH - nothing in JTR). You may or may not need that depending where you came from, but it's always nice.

EDIT: Also, ComfortFlex allows you a small personal item as well as the "full size" bag. That's basically anything that will fit under the seat. If you get a small rucksack you can transfer 5kg of stuff to that if asked. I regularly travel Flex with a 8 to 10kg bag in the bin and a 30L rucksack (half full) under the seat. Or even just have a carrier bag in your pocked that can become your 'personal item' if needed. I notice you're from the States - you'll be glad to hear than crew and airport staff are generally much nicer and more flexible here in Greece. Don't get me started about people I've seen boarding with three or four carry-ons including bags of large cakes, pets, wedding dresses... as well as two cases and a laptop!