Green’s Dictionary of Slang

a foolish person; a weakling.

1654		New Brawle 5: [A] suck-egg, a askall [...] one who would rob a Hen-roost, rather than pleasure a Wife.
1685		J. Crowne Sir Courtly Nice II i: vio.: I am told you hav been an Oxford scholar. cr.: A scholar, madam? a scholar’s egg— emptied by old suck-eggs.
c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Simon Suck-egg sold by his wife for a addle Duck egg.
1836		T. Haliburton Clockmaker I 28: He’s a regular suck-egg — a disgrace to the country.