You don’t give us your price range, but I assume it is in the Tyros 2 range, if so then most Jazz players (At least in the UK) go for the Korg PA1X Pro http://www.korg.co.uk/products/professional_arranger/pa1x_pro/pa_pa1x_pro.asp or Ketron SD1. http://www.bck.co.uk (The Yamaha and Rolands tend to be too staid to really pull off Full Jazz)
If you’re prepared to spend more, then go for an open keyboard like the Wersi Ikarus http://www.harmony-music.co.uk/ikarus.htm or Lionstracs Mediastation, http://www.lionstracs.com/store/ and get yourself the Garritan Jazz VST http://www.garritan.com/jazz.html and also the Native Instruments B4 VST, http://www.native-instruments.com/index.php?id=b4ii_us which will allow you to really get the Jazz beat going.
As to the weight issue, then I am afraid that the larger the keyboard, the stronger the case and support has to be, which of course means extra weight.
Hope this helps

Bill