Bring sugar and 1 cup water to a boil in a small saucepan over high heat, stirring until sugar dissolves. Chill syrup until cold, about 1 hour.
Purée syrup and 2 cups pineapple in a food processor until smooth. Set a fine-mesh strainer over a medium pitcher; strain, pressing on solids to extract purée. Stir in lime juice and remaining 2 cups pineapple. Divide among molds. Cover; insert ice-pop sticks. Freeze until firm. Dip bottoms of molds into hot water for 20-30 seconds to loosen pops. Remove pops and serve.
