I got a set of old hexes that were slung with 7mm cord. Should I redo them with the same cord? Or lighten it up with some 5 or 6mm ?
That is up to you. If you use 5mm make sure it made out of an aramad, Technora, Kevlar, Dyneema or other tech cord type material. I would not use standard nylon 5mm cordlette as you are looking at a breaking strength of around 9kN with knot efficiency loss. Granted 9kN is not bad, it is pretty hard to generate that much force on a standard lead fall, but if the hexes are rated for 12-16kN, you mind as well use material that will preserve that strength rating. If you use 6mm you are looking at around 11kN which is more appropriate. It seems as the manufacturer used 7mm because that is the smallest diameter nylon cordlette you can use that will preserve the hex's strength rating of 12kN, or whatever it is.