Battery for arduino zero project

Hi, I have an arduino zero project which almost requires around 2000mAh.
I was wondering what are my options to power my system other than the USB of course.
The lighter is the battery the better for my project.

Is there any shield available for zero? The only one I found is this one Adafruit PowerBoost 500 Shield - Rechargeable 5V Power Shield : ID 2078 : $19.95 : Adafruit Industries, Unique & fun DIY electronics and kits which i'm not sure if it works with zero.

Zero operates at 3.3v which makes it incompatible with some sources except those which use, e.g. the barrel jack, which i think has a regulator.

Thanks.