Why would they execute a fuel dump. If you look at the graphic you see a massive line of thunderstorms over the Carolinas and Mid Atlantic. You have to figure in that those storms were a bit further West than the graphic shows, but since they did not want to fly near them, it was probably their best route of flight. You also need to figure in how many other aircraft diverted around those storms. Perhaps, this was their best route of flight given traffic in the area, too. I highly doubt they flew West to fly East because of excessive weight and they're not going to just randomly do a fuel dump; they would be better off throwing money out the window in that case. Also, they more than likely had to execute a diversion to the West since the aircraft was probably not equipped to fly over the ocean since that path would have taken them beyond the gliding distance to shore.
Other than that, I think it's rather obvious they were avoiding bad weather. Radar doesn't show thunderstorms when it's a clear, sunny day.