It isn't just weekends that the popular trails in Yellowstone will be crowded, it's every day when they are a bunch of people in the park.  Hikers just don't show up on Saturday and Sunday.  However, as noted above, if you get off the real popular ones, you shouldn't be crowded.  When you get to Grand Teton, make sure you hike from Colter Bay to Hermitage Point on Jackson Lake.  If the trail is not closed for wolf babies, it's a great hike of about 4-5 miles and takes you to the edge of the lake looking out over Elk Island and up to Mt. Moran, one of the prettiest sights we have ever seen.  Also, make sure you take the Moose/Wilson Road and stop at the visitor center of the newest part of Grand Teton, the Laurence Rockefeller Reserve and take the very easy hike to Phelps Lake.  It's beautiful and well worth the trip, the Rockefellers took out all 30+ cabins at their place at Phelps Lake and turned it back to nature and it's almost impossible to see where the land had been used.  Also, a very nice hike is from the visitor center at Jenny Lake over to Hidden Falls and Inspiration Point on the far side of the lake.  Pretty easy hike but  spectacular views, especially as you get closer to the foot of the mountains and the falls.  Have a great time, Grand Teton is our favorite place to go in the summer, not because we hike, but because we fish Jackson Lake and sightsee all over the Park about three weeks each summer.