Good portable 5V 1.5A power source
Here's an example of a battery that partly fits the bill: -



Take a look at this - dimensions are 100 x 70 x 45mm and you require 200 x 150 x 50.

However, it weighs 1kg and not 500g

Cost is quite cheap but, it still needs a regulator to provide the power output. This is the sort of thing you need to decide on - cost versus requirements. The extra regulator circuitry would probably cost less than £5 from eBay by the way.