AR is Andrew Archer and the spoon has the date letter N for 1708/09.
On your Chester spoon RO is Thomas Robinson. I think that the date letter is T which would make the date 1719/20.
For valuation I suggest that you check Ebay’s completed auction listings for spoons of similar age and size. You should be able to find several London examples. However you will not find a Chester example there. Chester hallmarks of this date are vanishingly rare and I really don’t know where you can get a realistic valuation except through a reputable auction house.