While it's one of the primary complaints (after purchase), the market would seem to suggest that people prefer smaller/thinner phones in terms of purchasing decisions.
Sounds like Pentagram Monster series. The one I have with 4100mAh battery lasts for over 20 days, if I'm not using it heavily. And while it is heavier than typical smartphones, it's only about 1cm thick. As far as I know there's also a newer model with 6000mAh battery.