I disagree. From what John has said, he's fine. The shaft doesn't have to drip, and it won't necessarily score the shaft. To verify, put your hand near the nut when under power and see if it remains cool. If hot, then yes it's too tight.
In any case, don't try to replace the stuffing while still in the water. Do it on the hards.
For scads of research and anecdotes, go under Forums on this site and to Research wehre the Archives are.
Or you can follow this simple checklist.
Stuffing box on the hards, not in the water
REMOVAL
Unscrew thin brass jam nut to free up big one
Unscrew big brass nut completely.
Spray WD-0 inside to loosen up flax.
Turn corkscrew pick into first layer, pull Vise Grip offers better leverage
Repeat until all layers removed two if was chinzy, three more likely, four if anal
Clear out brass seating of any loose debris so new flax sits well
INSTALL
Buy 13 inches Teflon 1/4 inch = three at inches
Turn first wrap tight, mark with thumbnail or do at home with 1-inch stanchion
Cut with share razor knife or Dremel saw
Cut remaining 2 wraps to same size
Poke first one in clockwise by turning big nut slowly
Mark where it started with red pen
Screw down onto shaft to pack, by hand only
Loosen and repeat two more times
Do not overtighten, or will burn flax and not seat properly
TEST
When launch, be prepared to tighten using wrench keep jam nut loose
Should be no drips at rest, do not overtighten
In gear, should be no more than 1-3 drops per minute
Tighten one flat at a time while in gear
If the big nut is warm, back off as too tight burning the flax,unlikely at this point
Always retighten the jam cleat to avoid inadvertent loosening
When it’s right, try a day or week later takes time, be patient
Check again for three weeks then three months later
Should last three or four years okay to tighten one flat a time, over time