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The ad doesn't explicitly mention weight at all. The gist of the ad, rather, is that Christie used his power as U.S. Attorney to get out of some nasty driving tickets. However, instead of the phrase "used his power", the ad says "threw his weight around". In classic attack ad fashion, the ad closes on an unnatural slow-motion image of the opponent--only this time, he's getting out of a car--and well, jiggling.
Still, the real issue is, is it working? The answer is, very likely yes. As Engber points out, two separate polls by Public Policy Polling (.pdf) and the New York Times both confirm--independent voters are significantly less likely to vote for an overweight candidate.
Engbert accounts for this disparity (remember that more than two-thirds of Americans are overweight) with the following analysis:
...there's no constituency for a fat politician. Conservatives see excess weight as a sign of moral failing or a breach of personal responsibility. Liberals sneer at the bloated American lifestyle, even while imagining the war on obesity as a fight for social justice.