It is rare to see people care about power to weight ratios around here. This suggests to me that you may actually be serious about racing your car, or maybe not. The lightest weight Impreza's are the early ones (94-96) with power nothing.
If you look at something like what Subachad has done, you get good power for reasonable $$$'s. Because the early cars are 2500-2600lbs, he chose to go for around 240-250chp. For his track needs, that was adequate. He took an early WRX shortblock and put USDM EJ22 heads on it and incorporated it into his already assembled 1.8t kit. This could also be done with a complete early EJ20G longblock. These longblocks can be had for $650 out of CA.
From there you get a legacy turbo x-member, and a WRX downpipe and exhaust and drop it in. Change the wiring harness a bit to make it work with your factory ECU and then get an E-manage to run it. The whole thing can be done for around $1500.
You could also get a complete JDM swap with ECU for around $2000, but then you are in for the wiring, which you seem to want to avoid...