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Thanks for reaching out!
Since your Edison works just fine when powered through J1 and only reboots when powered through J16, we can conclude that this is most likely due to a power issue. As you may know Edison can indeed be powered through its USB port (J16) but this requires that the USB port used to power the Edison provides a steady output of 500mA (which is the standard for PC USB ports). However, this is not always the case. So, I would suggest you to try a different way to power your Edison, perhaps the hub you are using is not able to provide enough current to power the Edison.
Let us know how it goes.