Weaver Peak is also accessible from the valley floor. From Harrisonburg, take US 33 east past Elkton until you reach SR 628. Turn right, and follow SR 628 to the park boundary. Park here, and hike 1.2 miles on the Beldor Fire Road until reaching Skyline Drive. Turn right up the Appalachian Trail, and follow it to the summit. Total elevation gain is about 1,100 feet.
I see that makes sense as well.