The phrase "...is a suck" is a non-standard idiom, as can be seen on this Google nGram. In over 200 years of English language books to search, "he/she is a suck" cannot be found, and there's barely any instances of "is a suck" at all.
That said, even non-standard idioms can typically be understood by context-- otherwise new idioms could not be created. In this case, the context is defining the meaning: you should think of a baby suckling on a teat.
There is a similar definition found on Wiktionary.
suck (plural sucks)
(Canada) A weak, self-pitying person; a person who won't go along, especially out of spite; a crybaby or sore loser.
A sycophant, especially a child.