Too close to his best friend?

Well you're wrong to figure its "paranoid that they'll have feelings other than friendship for each other. " That might be accurate, that might be inaccurate. But if your his girlfriend, you're going to have to deal with that sooner or later.

But at less than two weeks it looks like you want to choose sooner. If she's truly his best friend, even if they never have more feelings than that, he will choose her over you at this point so don't overplay your hand. If you get what you want (distance between them) they'll both resent you. If you don't, well he'll reject you to preserve his best friendship.

You might let him know how much you'd like a date without any third wheels. Don't be all explicit that SHE can only see him one day a week or nothing like that. Rather, "hey it would be fun to go to this thing, just the two of us. " Keep on him until you get more of that alone time, but NEVER by pressuring him to reject his friend. ONLY by enticing him into the "extra" fun you two can have when unaccompanied. (and no it doesn't have to be sexual fun, but that might work. )

Your answer was written by yourself. "Alright, I just got into a relationship with an incredible guy a little under two weeks ago. " This "relationship" is only 2 weeks old and you want him all to yourself? I would gather that his friendship with this girl is considerably older than 2 weeks. You should feel like a third wheel, because that is what you are and will be until at least several weeks/months from now. His friend is probably also acting as a screener for him without his direct knowledge. She is looking out for him by being a de-facto chaperon on your dates. My advice would be to just go with the flow and be yourself. His friend will see your honest intentions and most likely (unless you are a weirdo or something) back off gracefully to allow you two to get closer and spend more time alone. However, be forewarned, guys who have a watchdog around them are common. It is uncommon for the watchdog to be another girl, and girls can be very vindictive when crossed. Guys would just punch him in the shoulder and say "better luck next time", whereas the girl could _______. (Fill in the blank - the possibilities are endless. )

Hard position to be in. It sounds like you just have to date him longer so you can become the three musketeers. If he likes you he will realize what he is doing. I would just suck it up for a few months and you grow closer.