Twit \twit\ , noun;
1. An act of twitting
2. A derisive reproach; taunt; gibe
3. A foolish, stupid, ineffectual person
1. To taunt, tease, ridicule, etc. with reference to anything embarrassing; gibe at
2. To reproach or upbraid
This word dates to the 1520's and is the aphetic* form of atwite from Old English ætwitan ("to blame, reproach"), which is a combination of æt + witan ("at" + "to blame"). Witan derives from Proto-Germanic *witanan, which comes from Proto-Indo-European *weid- ("to see"). The meaning "foolish, stupid, ineffectual person" is first attested as British slang in 1934 and it made the leap across the pond in the 1950's and 60's thanks to British sitcoms.
*Apheresis is a form of sound change that often involves the loss of an unstressed vowel, as with atwite > wit. Technically it is the loss of any sound, so all those word-initial silent 'k' words in English (e.g. knight) are also products of apheresis.