Agreed with Terisa that a Kobo would be your best bet.
If 6" is your thing, the Glo HD is indeed the best of the lot, even if it's discontinued. It weighs 180g.
At 6.8", the Aura H2O, at 230g
And although it's larger, it's not heavier than the above: at 7.8" the Aura ONE. I don't think it's too large to lug around, but I didn't think that of my 9.7"/536g Kindle DXG either, so YMMV