that's a little more than 2 ounces per day, as long as you're eating a relatively low fat diet otherwise, i think it's ok. however, check the label for the sodium, the spice may have a lot of sodium.
there are basically two categories of fats, saturated and unsaturated. you need both, but for the most part you want to minimize the saturated, because this is the artery clogging stuff. animal fats are high in saturated fat. also, some oils and fats are hydrogenated to make them more like a saturated fat (margarine), and they're bad for you as well.
some sources of unsaturated fats are nuts, seeds, fish oil, flax seed oil, etc. the sunflower seeds are much higher in unsaturated fat than saturated fat if you look at the label. unsaturated fats have EFA's (essential fatty acids) which are necessary for your body to function properly, that's why extreme low-fat diets are ridiculous. besides, fats make you feel full and may keep you from eating as much as you would otherwise, as Fausto alluded to.
if you plan to eat this many sunflower seeds for the rest of your life, you may want to educate yourself on fats. a book i've been meaning to read is "Fats that Heal, Fats that Kill". there are other things to consider, like the ratio of omega 3 to omega 6 EFA that you're consuming.