Another option would be to do the hike in one day. For me, I would rather do one long day instead two (or more) days schlepping a tent, sleeping bag, ground cloth, food, cooking paraphernalia, etc... Doing it in one day is a challenge, but so is schlepping all the stuff up the hill. I think you can get by with less than 10 pounds if you go for one day. You only need to carry one liter of water up to the switchbacks. There are many places to refill your water container up to the switchbacks. I use a UV device to treat the water, but many on this board drink directly from the source (check elsewhere on this board for the best places to refill). That way you do not need to carry much water until you get to the switchbacks, and by then you have lightened your load a bit (food). From the switchbacks you typically need three liters (5.5 lbs) to get to the top and back, where you will only need to carry one liter (again, refilling as needed along the way). So, total weight should be less than 10 lbs.
As other have mentioned, do not be worried about being alone. Odds are you will meet several new hiking buddies along the way.
