I would think that checking through your luggage should work out without problems. UA is tightly integrated with LH, and LH is tightly integrated with A3.
You definitely do not have to retrieve your luggage at FRA if it is checked through in the civilised part of this world - you clear immigration and customs for your hand luggage at FRA, and customs for your checked luggage in Greece.
It is possible that you would have to retrieve your luggage at ATH before your domestic flight - never had a domestic flight in Greece, so I don't know. In Sweden you have to do it, in Germany not, so there is no universal rule in Europe.
I definitely do not think that there would be a new weight limit if everything is booked on one ticket.
SmilingBoy.