Scandinavian Airlines has round-trip flights from Newark/New York (EWR) to Stockholm (ARN) for $448, NONSTOP. Flights October to May. Extended weekends available.
Some small OTAs on Skyscanner and Google have this for about $427; cheaper than the airline. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.
Carry on bag with a maximum weight of 18-lbs is allowed for free on SAS. You can avoid seat selection fees by accepting the randomly assigned seat at the gate.