1916, of obscure origin, many claimants. "One of the weird coinages of the airmen" [Weekley]. Common theory is that it is from designers' prototype nickname Type B-limp, in the sense of "without internal framework," as opposed to Type A-rigid; thus see limp (adj.).
An obese person
[1940s+; fr the WWI term for a nonrigid dirigible, based on limp]