Our rabbits are outdoors. We give the Mini Rex-(adult weight-3-4 lbs each)a 1/4 teaspoon (about 5-6 seeds) every other day during the coldest days. Our Flemish Giants (adult weight- 14-19 lbs.) are given 1/2-3/4 teaspoonevery other day. The oil from the sunflower seeds is excellent for their coats, especially in the dry cold of winter. Yes, the sunflower seedsare fattening, but given in moderation, they help outdoor rabbits maintain weight and condition.
I do know someone that gives their indoor bunny (a Mini Rex) exactly 2 sunflower seeds every other day, all winter long, because the vet told her too... the heat in the house is so dry, she has trouble with dry skin, scratchingand shedding. And it's worked wonderfully. But again, moderation is the important word here.
edited to add: I think a teaspoon is a lot for a 4-5 lb. rabbit.Although the rabbit will love it, I thnk it would do better with a little less. I sprinkle them on their pellets at night. They know when I'm serving them and rush right over and eat them right away!