A unit can perform a double attack if his/her Attack Speed (AS) is greater than the opponent’s AS by 4 or more. You’ll see a “x2” next to the attacker’s might (Mt) calculation in the Combat Forecast screen.
Attack speed is influenced primarily by the unit’s Speed stat but can be affected by the weight of his/her equipment. For the detailed explanation (and calculation) of how weight affects double attacks, please refer to this page.