You have not specified the lowest LCD size you will accept.
Of course you could get a Sony or an Apple with a 12.1" LCD and those are incredibly light. But those are not ideal for use outside of an airplane unless you get an external keyboard and/or monitor.
A lot of business level notebooks like the IBM's (great keyboards and light in noteobook that shines down on keys in airplane) and the HPnc6000 (business)--8.5 Cnet rating-- and Toshiba Techra series are 14.1" and about 5.5 pounds. But I think you may be saying you are willing to go smaller.
Fujitsu makes a nice 13.3" model. You can see this at Fry's Electronics if on the west coast or see them online (they are still made in Japan which is rare).
Sony has a plethora of smaller screen notebooks but they came in LAST in notebook and desktop service in a recent PC magazine poll. And, Sony's are always pricey for what you get unless you are totally in love with a product size and appearance no one else has (like the Sony ultralights from Japan which are not even sold here yet).
I would recommend you look for an Intel Pentium M (Centrino) notebook with a 13.3" or 14.1" LCD but you what size you actually want.
Stick with the standard XGA LCD resolution for your eyesight (not the more extreme SXGA or UXGA) -- this is the standard 1024x768 resolution.
Keep in mind if you get a true airplane ultralight like a 12.1" the size will be straining your eyes as well.
Many of these smaller notebooks have integrated (Shared video memory) video memory but if you really don't play any games or use demanding software it will be ok. But you can get the superior dedicated video RAM (also does not use up your RAM) on a 14.1" notebook like I mentioned at the top.
By the way, IBM came in #1 in that survey (Apple was not included or they would be there) as their notebooks are built more ruggedly and they have better service (they don't sell any consumer notebooks).
They will cost more than HP or Toshiba but they will stand more vibration and accidental drops.
Dell, HP, and Toshiba finished in the middle of the pack nearly equal but way above Sony.
I travel 100% of the time and I want to get a new laptop that is really light weight. I don't play any games and I doubt I would use a DVD for movies.
My work is mostly on the Internet and financial software. Also I am at that magic age where the eyesight is bit dim. Any suggestions would be appreciated.