"drunk," c. 1905, from some signification of blot (v.) in its "soak up liquid" meaning.
Entries linking to blotto
blot v.
early 15c., "to make blots (with ink), disfigure with blots," also figurative; mid-15c. "to blot out, obliterate" (words), from blot (n.). Related: Blotted; blotting.