Combine first 7 ingredients in a large zip-top plastic bag. Peel onions, leaving root intact; cut each onion into 4 wedges. Add onion, zucchini, and yellow squash to bag. Seal and marinate in refrigerator 1 hour, turning bag occasionally.
Drain vegetables in a colander over a bowl, reserving marinade. Place vegetables on a grill rack coated with cooking spray, and grill for 8 minutes or until tender; turn and baste occasionally with 3/4 cup of the marinade. Place the vegetables on a serving platter; sprinkle with the basil. Serve the vegetables with the remaining marinade.