How can fruits and veggies help with weight management?

Fiber/nutrition. Main advantage is giving the body what it needs nutritionally for metabolism. If you also substitute fast food/ preservative laden foods/ sugary starches and simpler carbs for veg-fruits your calories will decrease but more importantly your nutrition is much greater!
Bulk without fat. Fruits and vegetables are bulky and can make you feel full without as many calories as you would get from carbohydrates and fats.
Minimize fruit. Eat foods that are nutrient dense (like meat, fish, poultry, eggs, cheese, low starch vegatables and water) avoid foods that are not nutrient dense (like starches and sugars, including fruit) nutrient dense foods will increase your basal metabolic rate. On the other hand, starches and sugars impair thyroid metabolism via affects on your liver (which helps activate thyroid hormone).