It might not seem natural to feed a dog vegetables, but don't tell that to my canine compadre.
Replacing some of his more "empty calorie" biscuit treats with organic baby carrots has been exactly what the doctor ordered when it came to finding ways to bringing his weight down, without affecting the volume of his meals. I've tried just reducing the amount of food I put in his bowl and can tell you from experience that Rusty knows exactly how much kibble by count and weight that he's expecting. If I'm coming up short in either his morning or afternoon meals, he's sure to lead me back to his bowl, stare at it, and then look back to me to let me know that I'm not getting away with anything.
I need to provide a disclaimer that the first time that I tried to introduce carrots as a treat, it was unsuccessful. The baby carrot that I presented as a treat was snapped up, but before the chewing began, he put it down at my feet.
How did I change his mind?
I started eating raw carrots a bit more regularly myself. Before you could say "Rusty See, Rusty Do" he was waiting by the refrigerator for me to get a few carrots for him at snack time.
Like anything we eat, we learned that too much of anything isn't good for you. At 80+ lbs we found out that more than five baby carrots a day will soften his stool a bit. Each dog's metabolism is different, so your mileage may vary on this point, but I'd recommend starting with one a day and working your way up from there slowly. The point isn't to replace your dog's food with vegetables of any kind, but more to help reduce calories and add a bit of crunchy fiber to the mix.
To get Rusty's weight down, I'm replacing some of his food with a like volume of baby carrots several days per week. On those off days I may give him 2-3 as a treat instead of a more higher calorie treat. It's only been a couple of weeks, so it's hard to gauge progress, but he does have a bit more bounce in his step and his limp (as slight as it was) is gone.