Hi Joyce, Sounds like Bentley is in the middle of another growth spurt. I am of the opinion that it is most important to feed a growing puppy enough food to support his growth...
This is my thinking, also. He's growing, he needs more food to support that growth. As far as getting nutrition from the veggies, are you steaming them or pureeing them in a blender? If not, then no, he's not getting a lot of nutrition from them. Most likely just passing right through him. Plus, he gets a lot of exercise, so the added food during this phase is probably necessary for him. Three cups just doesn't seem like enough for his age and size. Even grain free, which is fed in much less
amounts than grain inclusive, calls for more than 3 cups a day for a puppy his size.
My general rule concerning puppies weight is to be able to see the last two ribs. I know on a Golden puppy they're more difficult to see, but you should be able to easily feel them. Even if you can't feel them, with him going to the food bin, it tells me his body is requiring more sustenance. Especially if this is a new behavior and he's doing it at weird hours.
I would at least try increasing his food and see what happens. I bet he won't get fat because his body will use up the added amount.