I too single dose. My girlfriend can only have decaf and I have decaf at night, so I can't keep the hopper full or half-full.
The tamper solution wouldn't work for me since the grinder's throat is too small. However,
after I made this mod last week I don't think that a weight is necessary. (For me, this mod totally makes single-dosing viable with this grinder.) A single dose of beans are in a very small column on top of one another and feed directly into the burrs; there's nowhere else for them to go but up, and the black divider thingy keeps that from happening. (Only closed part-way in the pic so you can see how much space 15.0 grams of Luna Nuova takes up.)

After reading this thread this morning I found something that is almost perfect as a weight, just to try it out.

It doesn't weigh very much and will sink down with the beans as they're ground to finally rest on the spinning nut at the bottom. However, I think it wasn't as good as not having it since a few very small pieces crept up the side, and I heard a little extra grinding than when I didn't use it. I then had to shake the pieces off and pulse the grinder to put them through.
An alternative to this is the small end of the plastic tamper that came with the Duetto. It's too big to follow the beans down because it rests on the top of the cardboard throat extension so it's not acting as a weight but it does reduce the distance out of the throat that a bean can pop by about an inch or so.

I'll play a bit with these a bit more but so far I don't think there's any difference that my limited experience/palate can detect in the cup.