having us on

I found nothing about the origin of the phrase "loose woman" in any of my reputable word and phrase origin fave sites, probably because it doesn't really need an explanation. The loose corset theory sounds like a folk etymology. Refering to someone of loose moral standards seems pretty upfront to me.

The late origin of "big shot" would seem to argue against any cannon salute explanation. Is there any evidence that cannon salutes were ever used for anyone other than a head of state or other highly placed statesman or military type? And even then, it's not the size of the shot but the number of guns fired that denotes rank.