12" screens use a little less power, but the difference gets offset by the slightly smaller batteries they use....
to put some number here, a typical 14"er (Merom/Yonah/Dothan) consumes around 18-20W under normal usage (e.g browsing with wi-fi on and medium brightness) vis-a-vis a 12"er which consumes 14-16 W under similar conditions....
but usually, the default battery on a 14" would be a ~60whr vs a ~55whr cell on a 12"
And yes, they weigh a lot less, and are much smaller in size (a4 sheet size usually) so if you do pick up a 12"er , pick up a good neoprene sleeve for 1K or so, and you can simply slide it in your backpack/handbag ...
Thus compared to a 15" or even a 14"er, they are incredibly more mobile