Thanks for the advice! So I ended up letting him have his way. We used HEAVY concrete planters, filled with concrete and topped with river rock. Guessing around 150 pounds on each leg. It stormed the other day - Super storm winds and rain from every direction and hail... I ran out and closed the curtains on the gazebo. With the curtains closed it held. With the curtains open, I believe it would have moved.
All I got to say is, I will never leave the house and forget to zip up that gazebo. It won't be my fault if it moves.
Heres a picture.