What's The Origin Of The Word Skinny?

With regard to someone who is thin rather than 'normal' or fat, it probably comes from "skin", someone who is skinny is skin and bones, more skin than anything else, see-through skin, etc.  In this context, it was in widespread use by the 1930s.

Skinny has another common meaning that comes from American English.  It means the simplest and most basic version of facts of a situation.   No embellishments or spin, just the true facts.  Skinny in this context has been used since the mid-1950s or earlier.   There is an Arts magazine for the Edinburgh and Glasgow called The Skinny.

Skinny also meant a ten cent piece (dime) in money in 1930s America. Presumably because it was so thin.

Skinny also means a sexy young woman in Australian slang, while skinny dipping means getting down to wearing just your skin whilst swimming.