Checking cabin luggage into hold
 

Does A3 help to check cabin luggage to the hold generally? Do they do it at outstation too? I am flying from CTA to ATH

Do you want to check your baggage in?

https://en.aegeanair.com/contact/?rdr=a_id%2F146

No generally, but when the flight is relatively full they ask passengers to check their cabin bags.

Short answer: Yes, they do.
I didn't even know that was a possibility until about 4 years ago, when I was kindly asked at the check-in counter to check my cabin luggage to the hold, due to the flight being full and the space obviously being limited. Since then I usually just ask them myself (if they don't beat me to it) and it has always worked out just fine, regardless of the airport.

You'll often get gate agents doing this too - coming around the boarding area and tagging larger bags for free gate check-in. I experience this a lot at CHQ and I've seen it at international outstations too (LHR?)

It's normal practice at LHR T2 for all *A members that the ground staff will proactively comb the economy class lines for rollers and anything else that looks too large and take them for gate checking. They also enforce the weight limits very strictly with scales at every gate.

It's a good thing and it speeds on time departure. A3 and TK are particularly strict there.