Line Releases

Cannon Quick Releases and a possible alternative

The Cannon Quick Release with its adjustable clamp

Cannon adjustable (2-22lbs) Uni-Release Pad pressure is set when the jaws are clamped shut Interlocking teeth with several positions give a range of grip strengths (I don't know if these have ever been used for falconry, though)

UK online supplier:

Tackle Bargains

Well-known online supplier (USA):

Cabela's: Cannon Quick Release

All of Cabela's releases
There are many different downrigger release clips, but these two by Cannon are both 'click' adjustable.