Will my dog develop respiratory problems if he remains overweight for an extended period of time?

There is a slight possibility, but unlikely. Of course keeping him at an ideal weight is important. I would have him evaluated by a veterinarian to determine his body condition score( this determines how overweight he is) so that they can recommend to you what foods he should eat along with his calorie intake. Bulldogs also are considered brachycephalic (shorter nasal passage) which unfortunately causes them to have a harder time breathing. His veterinarian may also recommend a surgery called stenotic nares, to open his nasal passages for better breathing.