We have been at WDW for a few days that week each of the last two years.
Compared to the holiday times when we usually visit, the crowds that week are like a walk in the park. A larger percentage of the crowd than usual may be from New Jersey, but the overall crowd seemed more moderate than large.
Like the site linked by a PP above, Touring Plans says that the crowd for Jersey Week is larger than the week before and after. I would think, though, that, especially over the weekend, it is difficult to separate the impact of Jersey Week from the impact of the Wine and Dine Half Marathon.
My advice would be that if you have the flexibility to go the week before or after Jersey Week and the Half Marathon, I would probably do that. But, if you do have to go that week and weekend, I wouldn't be overly stressed about the crowds.