some fighters gain 14lbs or even a bit more between weigh in and match time. Does this happen with heavyweights?
No. Because they don't have a we ight limit. They try to keep their weight at a weight they feel comfortable in but they don't "cut weight" like everyone else does. That doesn't mean they could eat burgers and crap all the time though
No need to, there's no weight limit, so no need to dehydrate/cut in the first place. It's also why heavyweight deaths in the ring are much more rare than in the lower weight classes, though to be honest, deaths from injuries in the ring are very rare anyway.
Not usually. Since there is no limit, they don't have to dehydrate themselves to meet any required weight. That is what the extra weight is on fight night...rehydration over night.