I built the circuit today with the 7805. The power consumption has gone up from 8watts with it's original PSU to 18watts. The 7805 gets really hot even with a large heat sink. I turned the voltage down to 7volts and the watt meter dropped to 8-9 watts. This confirms that it is the voltage drop across the 7805 that is using the extra power.
As an experiment I plugged the weather station and server into my old Belkin UPS. I took out the old 7ah battery and wired in my new larger 18ah battery. With the mains disconnected 0.6Amp was being drawn from the battery. Thats just under 8 Watts.
I would have thought using an inverter would be a very inefficient way of doing things.