Place both oven racks in middle positions in oven. Heat oven to 400°F. Cover 2 large baking sheets with foil or parchment.
Bring water and butter to boiling in saucepan over high heat. As soon as mixture comes to boiling, add flour, stirring vigorously with wooden spoon; beat until dough pulls away from sides of pan, about 45 seconds. Remove from heat; cool 2 minutes, stirring constantly.
Beat in eggs, one at a time, beating after each until smooth and glossy.
Using rounded teaspoonfuls, spoon dough, about 1 inch apart, onto prepared baking sheets.
Bake in 400°F oven on the 2 oven racks for 20 minutes or until puffed and golden, rotating pans from top to bottom halfway through baking.
Remove baking sheets from oven. Using a wooden pick or skewer, pierce a hole in bottom of each puff.
Turn oven off; return puffs to oven for 15 minutes or until dry and crisp. Remove the puffs to wire racks to cool completely.
Combine dill, sour cream and rind in medium-size bowl.
Slice top off of each puff and reserve tops. Scoop out any excess dough from center of each puff with small spoon or fingers. Fill each puff with 1 slightly rounded teaspoonful of sour cream mixture. Top with heaping 1/4 teaspoon caviar. Place cream puff cap in place. Garnish with dab of sour cream, dill and remaining caviar.