Here are some general rules when it come to sway chain adjustment:
For ground engaging implements such as plows and boxblades, landscape rakes etc. leave a 1-2" sway after centering the implement between the tires. Adjust left and right chains to center, and then lock them down with the nuts. It's good to use a wrench unless you have the jam nut (two nuts) type locks on your turnbuckles, otherwise they will loosen while you're working.
For PTO equipment, such as rotary cutter, tillers, etc., it's best to tighten the chains completely, leaving no sway in the implement.
If you have a problem with the chains tightening too much when you lift the hitch all the way up, and the implement was centered properly between the tires, the chains are too short and should be replaced. They should allow full movement from up to down position without a problem.
John