all a matter of total pack weight and fitness. I see no problem with a 7 pound tent if you know you can get to Trail Camp with a full pack within a reasonable amount of time. I've carried a 7 pound 2 person tent down the Muir Trail many years ago and thought it was a lightweight tent (it was, back then...)
There are much lighter tents available, but they cost significantly more. We use a 3-person Big Agnes Copper Spur for 2 - 3 person hikes and it totals 5 pounds. In winter it's an 8 pound tent for 2 people, or 5 pounds for a solo tent. All my recent tents are very tight for the number of occupants they are rated for, so a 3 person tent for space and comfort or room for two and a dog is a good idea.
If you have patience to look around, watch www.steepandcheap.com
(backcountry.com's outlet site) over the coming months. They tend to blow out Alps Mountaineering tents (I think that is their house brand) at steep discounts and they are pretty darn good for the money. Not much lighter than the Eureka you are looking at. Sometimes you'll even find higher end brands at good prices.
If you go in the summer, you probably don't really need a tent at all, but that's a different approach. I prefer a tent on longer trips as a haven of comfort at the end of long days in the middle of nowhere, while for a summer overnighter on Whitney a bivy and a close eye on the weather forecast would be just fine.