I bottled my first batch of beer about a week and a half ago.
Some slight carbonation has formed, but disappointingly little.
This sounds perfectly normal. I almost always have to try one after two weeks for fun, but three weeks at 70 is de rigeur. I have heard of people seeing full carbonation in even five days (yeast strain, temperature..?), but that's not my experience. Also, I recommend you put a bottle in the fridge overnight before opening, so that the pressure built up in the headspace has time to equalize, dissolving the CO2 into the beer.
A while back, a friend and I each weighed six different "3/4 cups dextrose" and the weights varied so much more wildly than I suspected it would. If you can afford a small scale (~$20?) you can dial your carbonation in much better for a given beer.
Let's look at a worst-case scenario:
You actually made 5.2g of ale, which with 12oz water for priming makes right at 6g, and that 3/4 cup weighed 4.2 oz instead of five, now you have about 2 gravity points instead of the wanted 2.6ish, depending on style. The best you can hope for then is ~75% of the carbonation you wanted (keeping in mind that somewhere around 33% is what we call "flat English beer"), so that "slight carbonation" you're getting, in some cases would be as much as you'll get.
Anyway, just give this one another week, chill and you probably have the carbonation you're going to get, assuming this wasn't a high-gravity beer. I bet it'll be fine. Maybe even great.