You know what? The initial tent you asked about is not a bad selection at all. The Eureka Alpenlite fits all of your goals EXCEPT the very lightweight part. It's 7 1/2 lbs, which is about 2 lbs heavier than I would want to carry on the AT, but if you're young and very fit, you can probably swing it.
On the AT my pack started at 44 lbs (including the weight of the pack and 5 days food) and ended around 32 lbs (including the same)- I shedded gear like crazy along the way. But my tent was 5.5 lbs (a sierra designs 2 person 3 season tent)- so 2 lbs more for the Alpenlite is not bad. I know some of the younger guys in great shape carried packs over 50 lbs- not for me and my 43 year old knees!!
FWIW- one of my camping buddies has the Eureka Alpenlite and he loves it.
For the price you can't beat it. But for more $$$ and less weight, I could recommend from experience-
the Nemo Losi 2p for around $340
http://www.powderfin.com/index.asp?PageAction=VIEWPROD&ProdID=457
the Marmot Alpinist for around $500
http://www.altrec.com/marmot/alpinist-tent
the Marmot is a
fantastic tent and for what you want, perfect, except for the price.
Sorry if I'm muddying the waters for you- if push came to shove I'd say-
- if price is more of a concern than weight, get the Eureka that you were first looking at
- if weight is more of a concern than price, get the Marmot
- if weight is REALLY a concern- get 2 tents, a 3 lb-er for the AT and a heavier tent for winter