By going with full fuel when your solo the GC will move aft because the fuel tank or tanks are in simple terms towards the back of the aircraft. So this is not a good idea if you very light and solo and may end up putting you out of CG limits.
This is precisely the reason that the minimum solo weight for the R22 is 130lbs with only the main tank fiulled, but 135lbs with full fuel. I have such a hard time getting some students to understand this!
However, even though I'm above the minimum weight with full fuel, I'm pretty close to it, and I find the R22 flies uncomfortably nose high when I have full fuel. So yes, it's quite OK to put stuff under either or both seats. I believe in having useful ballast, so I usually have a very full flight bag with everything I could conceivably need, plus spare oil. But anything will do really. And if you're going to pick someone up later, take a large plastic container of water; then you can empty the water when you pick up the passenger.
We lightweight pilots who've been doing this for a while have got it all worked out.
