Plain and simple; they don't want you to have sex. that's it. The things that bothered them were you being in her room, and her being at your house. granted, i believe you respect her and your religious beliefs and aren't planning to have sex now, and of course if you wanted to you could go other places, but they're being overprotective. They can't control her, but they try to limit the temptation. I am only 22, and my gf is 3 yrs younger. those 3 yrs can be huge, specially from 16 to 19, and 19 to 22. they don't trust you enough, especially with her being 16 and you being older and out on your own. and it may be her they're punishing, not you. you didn't bring her to your place, she came there. you are older, and being on your own, older in other ways, you need to be in control. you must force her to follow her parents wishes, do what is right, and trust that in time it'll be easier. you may know you want to be with her, but at 16, how can she know? if you truly love her, be with her but let her be 16 too. after another 6 months and another 6, things will be easier, you just have to be patient, and respect her parents, knowing that they are in charge, and can indeed keep you 2 apart. of course that's stupid of them, since it will only drive her to you. anyway, there's a few different issues there, but it's basically this: if i had a 16 yr old daughter, no way in hell i'd want her at her 19 yr old boyfriends place alone. i wouldn't take their steps, but they responded in this way.
good luck,
-----Krugger