more worrying was that roll/yaw tendency of the plane...
I have never flown a C152, but in other equally small planes (DR200-120 for instance) the big bloke in the RHS makes all the difference. So you're flying dual, no roll/yaw tendencies at all. Perfectly balanced, hands-off. But when you fly solo, continuous pressure on the stick or yoke is required to keep the plane level and balanced. To relax your arm muscles every now and then, you can keep the airplane level with a bit of pressure on the rudder, but the aircraft won't be perfectly balanced then.
If you have an in-cockpit adjustable rudder or aileron trim it will help a lot (although the rudder trim in the PA-28 seems to be next to useless in this respect) but otherwise you'll just have to deal with it.
In general most clubs/schools seem to have a policy not to fiddle with fixed trim tabs at all, since you're likely to make things worse rather than better, unless you actually do a comprehensive flight test program consisting of multiple short flights to evaluate balance, with tiny adjustments in between, over the whole loading range. Not something the average student/renter is willing to undertake.
(Wow, eleven posts in a sternone thread and nobody has mentioned the M-word yet!)