Generally speaking, the larger the diameter and width of the wheels, the heavier they are. I haven't weighed my new wheels yet, but I doubt they would be any lighter than the stock 19's. They may be about the same given that the stock 19's are not exactly lightweights. If you wanted maximum weight savings, a smaller diameter rotary forged or low pressure cast wheel would be your best bet.
Thanks Chris, a stiffer rear sway bar would have the effect of reducing understeer, so it would actually compliment a staggered setup well. I put a thicker rear sway bar on my previous Subaru WRX, which was too understeery in stock form, and it really helped with the handling balance, especially on the track.
Mine is AWD as well and I haven't noticed any issues with the staggered arrangement. As long as the tyres are the same diameter, it shouldn't be a problem as far as I'm aware. The 245/45 and 275/40 are nominally within about 1mm of each other in terms of diameter, which should be well within tolerance of the AWD (and TPMS) systems since they would need to account for variations in tyre wear and manufacturing tolerances.
Probably the main drawback of staggered tyres is the inability to rotate them, so I'll have to see how things go as they wear.