For my MR2 I put in a Scorpion Stinger 7.8Ah lithium ion battery which weighs 3.6lbs thus shedding about 23lbs, but then I measured the standby current of the car and found that the car was drawing 48mA* while off, thanks to the aftermarket gauges and alarm. Since the battery shuts itself off after it reaches 5 or 10% charge (I forgot which), I essentially only have around 150 hours of standby time before I need to jump the car. I spent a few days pulling stuff out and sorting out some wiring, and managed to get the parasitic load to under 30mA by shedding some alarm stuff, but that's still not enough.
(For the record, if I had to do it again I would have gotten this battery for its higher capacity but at the time I didn't know the price was so good:
LiFePO4 Prismatic Battery: 12.8V 20Ah (256Wh, 10C rate) with LED Balancing - UN38.3 Passed (DGR))
I thought about getting the Harbor Freight battery charger, but I was worried the regulator on it wouldn't be very good and it could possibly fry the battery, so I ordered some 53mmx30mm 5V solar panels off Ebay for 86 cents each, and put 3 in series with a diode, and taped it on my dash like so:
They claimed "40mA", which I thought was 40mA at 5V...unfortunately that was not the case. Open circuit voltage is 6V in bright sunlight, and I was getting around 28mA with the panels shorted out in direct sunlight, and under my windshield with direct sunlight it produces a little over 10mA when the sun is bright, so this charger unfortunately doesn't really put a dent in my battery drain.
The good news is that because I bought these individual 5V panels, I can resolder 4 of them together with bypass diodes and get 23.5V (the diode has around 0.5V drop) in bright sunlight, which will charge my 13.2V lithium ion battery at near maximum efficiency when it's bright out, and should provide at least some juice for perhaps 8 hours a day. Thus I ordered another panel for 86 cents and will be putting 4 of them together shortly.
If I were to do it again, I would buy 2 "12V" panels off Ebay (I think someone sells a set of 2 for 6 dollars right now), put them in series, and call it a day. The 12V panels are a good bit bigger, but it really doesn't hurt to have a net charge going to the battery during the day since it will drain it back down at night. Even then, those 12V panels are never going to overcharge the battery when any keyless entry system draws over 20mA.
I think any non-plugin hybrid car would be well served by this mod because always cycling the battery will hurt your wallet pretty badly by reducing the lifespan of the battery considerably, and the engine needs to work harder to recharge a dead battery. For 4 dollars worth of materials and parts, half an hour of soldering and such, then a bit more time to figure out the wiring, this is pretty low effort especially if you are familiar with how to tap into a constant 12V source in your car.
* As a disclaimer, I think my amperage readings are kind of wrong because my multimeter reads drastically differently between the 10A and 200m settings, so I think I need a clamp on ammeter for more accurate readings, but I think these are pretty reasonable estimates.