"young mammal before it is weaned," late 14c., agent noun from suck. Slang meaning "person who is easily deceived" is first attested 1836, American English, on notion of naivete; the verb in this sense is from 1939. But another theory traces the slang meaning to the fish called a sucker (1753), on the notion of being easy to catch in their annual migrations. Meaning "lollipop" is from 1823.
To be in trouble; be in a bad situation (1970s+ Army)