what living creature weights 800kg in the morning 500 kg in the
afternoon 5g at night.

One of the Greek Gods with the ability to change his appearance?

Come to think of it, the Greeks didn't use kg!

Their Dry Measures were: 

1 medimnos = 48 choenikes; 1 choenix = 4 kotylai; 1 kotyle = 6 kyathoi

Are you sure that it is a Riddle, and not a Sieve? 

One of the Ancient Greeks, Eratosthenes by name, certainly had a Sieve.

An ox at a spit roast?

A Fisherman!

He weighs his catch first thing in the morning;

After cutting out the unwanted bits, he weighs it again in the afternoon;

Then, at night, he weighs out a small portion for his supper.

Sounds similar to the Riddle of the Sphinx:
"What animal has one voice, but goes on four legs in the morning, two
legs at noon, and upon three legs in the evening?"
"Man, who in childhood creeps on hands and knees, in manhood walks
erect, and in old age with the aid of a staff."
http://www.nmia.com/~sphinx/greek_sphinx.html

answerfinder-ga

'Do I find myself disagreeing with the Mighty Answerfinder?' I ask myself.

Yes, 'fraid so.

This Riddle is NOTHING like the Riddle of the Sphinx!

C'mon admit it ...