Where did the term "at‑large" originate from?

"At large" is not hyphenated in this context (the suspect is at large). But there are phrases such as "ambassador-at-large" where the entire phrase is hyphenated. This means something like "a roaming ambassador", i.e. one not attached to a single country, but who plays a wider global advisory role on an issue. ("Ambassador-at-large for human rights", etc.)

Large is an old sailing term - (actually, we still use it on tall ships. When the wind is behind your boat (abaft the beam), it is called “sailing large.” In this favourable 'large' direction the square sails are set and the ship is able to travel in whatever downwind direction the captain wants, so “at large” would mean free to run with few obstructions - like a criminal at large. (The opposite of "sailing large" is calling sailing “by the wind” or “by the bowline,” and involves using the non-square fore and aft sails to tack into the wind. The sheets (lines attached to the control corners of these sails) are tied with bowlines ( bowline is pronounced bolin) . So, a trip planned to include both upwind and downwind sailing would “by and large” get you to your destination.

At large has been used to define, "as a whole". When you use the word, "large", it automatically encompasses somewhat an imaginary definition of "very huge" or "very big". The power of a word, when spelt out, is so strong that in a trice, it invokes the hidden meaning of that particular word. Suppose you tell a child that "I will give you a small piece of bread", then, it may scowl its face, as not being satisfied. On the contrary, when you say that "I will give you a big piece of cake", its face will be blooming with smiles. This is how the expression of words acts as an incentive or disincentive. Similarly, "at large" is used both in positive and negative ways (e.g. The fugitive was at large or He is an Ambassador-at-large" like Henry Kissienger.). Similarly, words, depending on their usage coupled with circumstances, may invigorate. There is a very good couplet in Tamil language, which asserts that the wound inflicted by a word can never get healed whilst that caused by fire will get cured sooner or later.