Wobbly (n.) Look up Wobbly at Dictionary.com
1914, member of Industrial Workers of the World (I.W.W.). Probably some sort of elaboration of the W aspect of the acronym.
wobbly (adj.) Look up wobbly at Dictionary.com
1849, wabbly; see wobble (v.) + -ly (1). Form with -o- is from 1851. Related: Wobbliness.