"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; 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 (the fish so called from the shape of its mouth). As a type of candy from 1823; especially "lollipop" by 1907. Meaning "shoot from the base of a tree or plant" is from 1570s. Also the old name of inhabitants of Illinois.
"a quick blow, dig, or thrust with the fist," by 1570s, probably from punch (v.). In early use it also could refer to blows with the foot or jabs with a staff or club. Originally especially of blows that sink in to some degree ("... whom he unmercifully bruises and batters from head to foot: here a slap in the chaps, there a black eye, now a punch in the stomach, and then a kick on the breech," Monthly Review, 1763).
The figurative sense of "forceful, vigorous quality" is recorded from 1911. Punch line (also punch-line) is from 1915, originally in popular-song writing. To beat (someone) to the punch in the figurative sense is from 1915, a metaphor from boxing (attested by 1913); punch-drunk "dazed from continued punching, having taken so many punches one can no longer feel it" is from 1915 (alternative form slug-nutty is from 1933).