In a medium saute pan over medium heat, add vinegar, sugar, and honey. Let simmer for 15 to 20 minutes or until reduced by half. Keep warm for glazing on grill.
In a 1 gallon re-sealable bag, add the balsamic vinegar, olive oil, sea salt, pepper, and garlic and mix until combined. Next, add the carrots, celery root and onions, remove excess air. Allow to marinate for 30 minutes. Then add the zucchini and squash and allow to marinate for 10 more minutes.
Preheat grill to medium-high.
Brush grill with oil. Add onions, carrots and celery root. Cook on both sides for 3 to 5 minutes brushing with balsamic glaze. Mark and brown evenly on both sides. Remove to holding pan and cover with aluminum foil. Add squash and zucchini to grill, brush with glaze and cook for 2 minutes per side, until marked and evenly brown. Remove to holding pan, and cover until service.
Drizzle veggies with remaining glaze and serve on a warm platter.