a common 18c. colloquial term for "homosexual man" or "man who is deemed effeminate, a sissy," by 1707, perhaps 1690s. The fem. proper name Molly or Moll served as a type-name of a low-class girl or prostitute in old songs and ballads (perhaps in part for the sake of the easy rhymes).
But the colloquial word also resembles Latin mollis "soft," which also had been used classically in a specific pejorative sense in reference to men, "soft, effeminate, unmanly, weak," in Cicero, Livy, etc. A 1629 publication from the Catholic-Protestant theological disputes, "Truth's triumph ouer Trent," written in English with swerves into Latin, at one point describes the denizens of Hell as fideles fornicarios, adulteros, molles, and so forth, and molles is translated parenthetically in the text as "effeminate." Molly House as a term for a brothel frequented by gay men is attested in a court case from 1726.
seabird, 1857, short for mollymawk, mallemuck, from Dutch mallemok, from mal "foolish" + mok "gull."