I've found the Vera Bradley Disney Hipster to be the perfect park bag now that kiddos are older and we need less "stuff". I only pack a very small first aid kit (tylenol, band-aids, and spray neosporin), a travel size anti-bacterial (germ-x / purell), a full size spray sunscreen, a face stick (sunscreen), chapstick, a small brush and hairbands, 4 disposable ponchos, cell phone with portable charger, pen, and ID. Oh! and park map/times guide!
I do have to switch shoulders every now and again, but it doesn't get terribly heavy. It's as much about what you put in the bag as the bag itself.