In a large, heavy-bottomed pot, heat oil and kernels over high heat, uncovered, until first pop. Cover and remove from heat for 1 minute. Return to high heat and shake until popping ceases. Sprinkle with salt and shake to distribute evenly. Measure 3 1/2 cups of popcorn, and reserve.
Place sugar in a saucepan and add enough water to cover. Cook until caramelized and golden then stir in the reserved popcorn and peanuts. Pour onto greased sheet pan and break up slightly into clumps.