I think the answer is clear: no. I also think the question deserved to be asked.
My own history with obesity is here, in all its gory glory. Fat stigma is an anathema to me, and I wish that we could ignore the issue entirely. We can't. And that means that the fat of Christie's will inevitably bleed over into the zone that perpetuates stigma and stereotypes. We have to find a way to judge Christie's weight in the context of what the job of being presidential entails, and then, at the same time rigorously segregate it from any other type of judgment. If we can answer the question, then we ought to accept that answer and move on.
Christie himself has acknowledged that his weight raises the probability that he will acquire debilitating medical conditions, and has thus admitted to the public square a fact about his body that requires communal judgment. We should base our judgment on independent assessments performed by doctors. Should Christie run for president, he will submit himself to an examination, and when the results are known, they ought to be debated.
Is Hillary Clinton too prone to blood clots to be president? No. But the question will be asked and ought to be asked. Health matters. Endurance, as a quality of health, matters more than other qualities, like the propensity for certain types of cancer. Christie has proven by his actions as governor that he can endure a punishing schedule. Being president is tougher than being governor. It is stressful. Being overweight in high-stress jobs is not pleasant, it taxes the body, and it increases the likelihood that he'll have a heart attack. (He's not a ticking time bomb; the actual chances of any one person who is fat and in a stressful job having a heart attack are not insignificant but not necessarily in the realm of "likely" either.)
It is not entirely instructive to look to past presidents who were overweight; Teddy Roosevelt's body type and lifestyle are not comparable to Christie's. The eras are too different. But it might be helpful to realize that as president, Christie would have medical care second to none. He'd have a doctor with him at all times. His diet would be monitored rigorously. The chances that he'd stick to an exercise plan and a medication regimen designed to mitigate the effects of his obesity are high. And that would reduce the likelihood of any sudden problems.