Green’s Dictionary of Slang

(US) a second-rate brand of cigar.

1894		T.B. Searight Old Pike 144: They [i.e. cheap cigars] became very popular with the drivers, and were at first called Conestoga cigars; since, by usage, corrupted into ‘stogies’ and ‘tobies’ [DA].
1903		Westminster Gazette 23 May 10/1: The railway ticket office clerk twists and swigs at a ‘toby’ as he asks you ‘Where for, sir?’ [DA].
1974		R. Blount Jr About Three Bricks Shy of a Load 231: All through the trip the three of us smoked excellent cigars the size of Joe Greene’s fingers [...] The Chief called these cigars ‘Tobies.’.