I wasn't exactly looking for a stud, was hanging a frame so I just used anchors. Drilled 3/16" holes for the anchors, but I am pretty sure I hit a stud. If I did indeed hit a stud, and somehow drilled at the edge of it, could I weaken it or do anything that could matter? What would be the biggest hole you can drill through the stud near the edge without weakening it?
Any hole will weaken it. That sized hole is unlikely to weaken it enough to matter (I've see bigger knotholes on the edge of graded framing lumber, for instance.) Particularly if drilled to proper depth (you should not be drilling more than 1-3/4" into a wall, so 1.25" into framing with typical 1/2 sheetrock, without knowing EXACTLY where your hole is going, due to the way plumbing and electrical codes are written for wire and pipe protection.)
Always a good idea to look for studs when drilling walls, whether to hit them or miss them.
About 1/2 inch for a notch, 1/3 of the thickness.
Usually no problem for a stud.
There can be a big problem if drilling into a wall and hit an electrical cable/wire, which can be near/on/in a stud.
Electrical cables or pipes closer than an 1 and 1/2 inch to the face of a stud should have a steel plate protecting them from screws/nails. Electric cables going on the side will not have this protection.