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."