2 hour connecting Flight enough for DC-Rome-Athens

A 2 hour 30 minute layover sounds ideal. You will only go through immigration and make it as long as the first flight arrives on time. If the first flight does not arrive on time, the airline is liable for putting you on the next flight with available space to Athens.
Just put any thing in you carry on bag (e.g. medications) and/or "valuables" that you can't live without if your checked bag was delayed.

I hate to be "that guy' but I am. On a flight out I never check my bag. I travel light and have one small (of late a RS backpack) carry on that does not leave my side until I get to my destination. A checked bag that does not transfer or arrive can be a nightmare. I once watched a small flight from the UK to Ostend load up without my bag. I told the agent at the airport that my bag was missing. His response, "deal with it in Ostend". Have you ever been to Ostend airport? There was not a single person present, a single office open when we arrived there. I was on three week trip and spending the night in Brugge. I had to return to that bloody little airport 4 different times over a period of 3 days before I got my luggage.
Or, the time my bag went to Appleton while I got stranded in Detroit and then the next day in SF on my way to Asia for 4 weeks. That was the night that I learned that bar code scans were not actually being used to track a bags location. I arrived 3 days later in Zhongshan with a fresh shirt I bought in the Hong Kong Ferry terminal. Six days later my bag arrived.
Or the time I ended up in Penang without any clothes and a promise from Singapore Airlines that they would reimburse me for any clothes I needed to buy. Hello, shirts, socks, underwear....all from small local shops...
The absence of luggage on arrival is an annoyance. The time it takes to correct the problem and the hassle of making claims, calls, following up is a nightmare. The airlines have trained me not to check my bag or anything of any value on an outbound leg, ever.
On the way home I check my bag but I don't check anything important in it.....there was the time I inadvertently checked my car keys. Naturally the bag was delayed.
You have more than enough time for your transfer but don't be so certain of your bags arrival unless you are physically carrying it with you.

2.5 hours sounds like a best-case option to me.

Mishandled (includes lost & delayed) bags are down by 50% over the last decade while airline embarkations have doubled. Can lost bags happen? Of course. Should you worry about it? Only if you're looking for something to worry about. (Or maybe if you have a 35-minute connection somewhere.)

I can't be bothered with them, but then I am old school...but there are GPS trackers that can be attached to luggage if you are stressed about it. I can see them being useful if you are headed for a safari or cruise...and yes, I have agonized over both, but you can also just do what we used to do 'in the old days'....take one or 2 changes of clothes in your carry on bag.

Mack seems to have been exceedingly unfortunate in his checked bag experiences. I’m sure that somewhere one can find the statistics on this issue, and that the chances are really low that your bag won’t arrive with you or by the next morning. For what it’s worth, I’ve been traveling to Europe since the early ‘70’s, and only a couple of times even had to wait until the next morning for my luggage. To prepare for that remote possibility, I pack toiletries, essential meds, something to sleep in, a change or 2 of underwear, and a change of clothes into my carry-on. And don’t forget to include your house and car keys on your return trip.
The airlines used to provide an emergency pack for travelers whose bags didn’t arrive. I don’t know if that’s still true.*
To get back to the original question, I’d go with the 2.5 hour layover. Since there is a later flight, you’ll have that safety net.
*Here’s a chuckle for everyone. My brother and sil once arrived in Paris, but their bags did not. Air France’s emergency packs consisted of oversize T shirts to sleep in, dental kits, several kinds of perfume, and a package of condoms. Oh those French!

Frankly I don't think that my travel travails are particularly exceptional. Most folks who travel frequently have stories to share. In my case with North of 2.8 million miles on major carriers and an unknown number of miles on regional flights (does anyone remember Kingfisher Airlines?) I have quite a few. Due to the numbers of miles I wracked up I am fortunate to have been extended several useful lifetime privilege's including priority baggage handling and upgraded seating. It matters not. When you look out the window of the plane in Dulles and see your priority tagged bag sitting outside in the driving rain waiting to get loaded there is not a thing you can do to wish your clothing dry.
Baggage handling and tracking has improved..that is a fact. It has gone from terrible to mostly acceptable. But it is not infallible. If you trust the airline implicitly it is only a matter of time before you arrive at your destination sans luggage.
If you have planned travel that does not allow you to dwell for several days waiting for your kit to arrive take note and plan accordingly. There are only so many extra socks and undergarments you can jam into your computer bag. Been there, done that.
The courtesy bags vary by airline....you can always count on a toothbrush and tiny tube of paste. Some offer a razor, comb, nail file....I've never been offered a shirt or prophylactic's...that must have been first class service.

If you miss your connection with the 2.5 hour layover do you default to the 7 hour? If so, you've got nothing to lose by booking the 2.5. I'd book the 2.5 even if you have to scramble if the connection is missed.

Thank you for the assistance. It sounds like 2.5 hrs is good. If not, then the airline will put me on the next flight, in which case, I have shaved off 2.5 hrs of the 7 hr layover.

I would think that 2.5 hours is plenty. Regarding checked baggage - as I rule, I do not check bags going outbound. Too much of an inconvenience if something should happen and bags are lost or delayed. I typically check bags when I head back stateside.

Also, you state that you booked Delta via Alitalia. If you are on a Delta flight, you will be in terminal 3 in FCO, and will depart from there as well. That is, if BOTH are Delta flights. If they are Alitalia, you will probably land in Terminal 3 but you could be in Terminal 1 for the Athens leg on an Alitalia flight.

2.5 connection should be fine, particularly with the 7 hour backup. The airline should rebook you if by chance you miss the connection; the only way that might happen is an equipment delay on your initial outbound.
Also, United has recently announced they are allowing more flexibility in delaying departures to accommodate connecting passengers whose arrivals have been delayed. I expect other airlines will follow suit. That should also work in your favor.

I think that 2.30 will be sufficient mainly because of the time of day -- at 7 am, there is less traffic in all European airports. After lunch air traffic builds a lot, and delay in the plane getting from airstrip to an open gate, can create delays.