c. 1400, endosse "confirm or approve" (a charter, bill, etc.), originally by signing or writing on the back of the document, from Old French endosser (12c.), literally "to put on the back," from en- "put on" (see en- (1)) + dos "back," from Latin dossum, variant of dorsum "back" (see dorsal). Assimilated 16c. in form to Medieval Latin indorsare. Figurative sense of "confirm, approve" is recorded in English first in 1847. Related: Endorsed; endorsing.
You can endorse, literally, a cheque or other papers, &, metaphorically, a claim or argument, but to talk of endorsing material things other than papers is a solecism. [Fowler]