I didn't offer any particular advice there, only suggested his fears may be rational; but it's an important caveat that merely because a belief is rational doesn't make that belief correct, which I suppose I should have been more clear about.
It sounds to me like the real basis of his concern may be the fact that he's making unreciprocated requests. I have no in-depth knowledge of the situation, so I'm merely hazarding a guess here, but if he's the one arranging all the dates (or whatever), an alleviation of his fears would require her to take a more active role in the relationship. Which may require having a serious discussion admitting his anxieties and the reasons for them. An arrangement where she has to plan every other date, or whatever, might suffice.
I've experienced a one way relationship before (see http://lesswrong.com/r/discussion/lw/gtv/need_some_psychology_advice/8j5k) and I really don't think that's what's going on here. I think she has a perfectly reasonable and appropriate level of interest and involvement concordant with someone she's been dating for two weeks, and I have an unreasonable and inappropriate level due, once again, to my brain chemistry and/or personal history. Calling things off right now would be a terrible idea because 1) I really have no reason to think it won't work and 2)...
I started going out with a fantastic girl a couple of weeks ago. Everything is great, except that whenever I've sent her a text message or email requesting something and haven't received a response yet, I experience significant dysphoric anxiety, fearing that her response will be not just "no" but "no and I don't want to date you any more". This is due to brain chemistry or personal history, take your pick—either seems like a possible explanation to me. But there's certainly no evidence supporting the idea that this is likely to happen, nor is the anxiety helping me prevent it or helping me in any other way.
Does anyone have evidence-based advice, or pointers to same, on dealing with this kind of issue? It is the only splotch on what have otherwise been the best two weeks of my life.