The mp1550 weighs pretty much nothing, the weight is 4 AA batteries.
Edit:
Just looked it up, the mp1550 is 4.5 oz by itself. I would say that the weight of the 4 AA rechargeables is easily 90% of the weight once the batteries are in there.
It's also pretty small, there's a good pic in this "review" with the back cover off so you can see the AA batteries:
http://www.slipperybrick.com/2008/01/tekkeon-tekcharge-mobile-power/
It seems to work fine using alkaline batteries for low power draw devices (think anything that draws 500mah or less), but iphones, droids, etc, definitely have to use high end rechargeables.
Not sure how the eneloops will do, aren't those low discharge batteries? I don't have any low self discharge batteries to test against, so I'm not sure how much current they can handle, but it's probably pretty close to the powerex non-low-self-discharge batteries (pheww).
I think eneloops are 2000mah, whereas teh powerex ones are 2700mah (supposedly, I think they're more like 2500mah).