RE: How tight should the nock be?
Tight nocks are detriment to accuracy. They tend to make an arrow act stiffer leving the bow. Probably some other factors as well.
That being said, you should be able to nock an arrow, hold the bow horizontal with the arrow hanging toward the floor (ground), then give a decent tap on the string and it should fall off. Maybe just a tad tighter for a hunting setup. But when nocked it should also slide up or down, being slightly loose on the string.
So how do you accomplish this? IMO, after many decades of shooting, is to find what serving size fits the bill and have the center serving replaced. Some guys say heat the nocks in hot water and spread them by fitting them on the string. Some will say to file the groove a little wider, but these methods leave room for error. You can NEVER file two nocks absolutely identical.
FYI serving comes in different sizes (diameter). Usually you see .018", .021", .022", .026" or very similar depending on the manufacturer (Brownell or BCY).
There is no cut and dry answer as to what size to use. Strings themselves can vary depending on what material is used or how many strands there are. Different nocks vary a little too, but not much.
Any competent bow shop should be able to do the job for about $5 or so. They would best be able to figure out what size to change to.
Hope this helps.