I remember checking out the PSR-F51 in a music store a while back. I remember thinking that it seemed like it would be for someone on a very limited budget who wanted to get a keyboard with full-sized keys without going with a keyboard of unknown quality from a "no-name" company, but that for about $20 more, the PSR-E200 series keyboards were probably better. However, I was not considering the weight and portability of the keyboard, so that maybe the F51 weighs less.
Yamaha's website has the PSR-E273 weighing "8 lb (4.0 kg, 13 oz) (not including batteries)" -- whatever that means (looks like they're mixing English and metric units -- the English-unit weight is likely 8 lbs, 13 oz), and the PSR-F51 at "3.4 kg (7 lbs 8 oz) (not including batteries)", so it appears that the F51 is, indeed, lighter, though not by a great amount.
Then, of course, there is also the little PSS-F30, which is basically a miniature PSR-F51 (right down to the color scheme of the control panel), but of course, that has mini-keys and would not really be suitable to learning how to play keyboard or piano.