Phrase finder suggests that the saying originates from the dictionary definition of the term "suck-egg" which refers to:
- An animal that is reputed to suck eggs, e.g. a weasel; figuratively. an avaricious person.
It is also considered to be a dismissive insult similar to the term fuck off but is less abrasive.
TL;DR
It's a less-abrasive dismissive insult intended to be directed at someone who is being greedy.
Carl:(eating a tub of pudding)
Jane:...(saving two snack packs of pudding)
Carl: "Can I have some of your pudding?"(still eating his pudding)
Jane: "Go suck an egg."
Used to tell someone to leave you alone Synonyms: fuck off, get bent, (go) kick rocks, etc
A: hey dude, did you hear about those rumors?
B: what rumors?
A: the one where you were cheating on (C) with (D)
B: how do you know?
B: (E) told me
B: oh well (E) can go suck an egg, I’m sick of their shit bro