We present a magnetotransport study in an InAs/GaSb double quantum well structure in the weak localization regime. As the charge carriers are depleted using a top-gate electrode, we observe a crossover from weak antilocalization (WAL) to weak localization (WL), when the inelastic phase-breaking time decreases below spin-orbit characteristic time as a result of enhanced electron-electron interactions at lower carrier concentrations. The same crossover is observed with increasing temperature. The linear temperature behavior of inelastic scattering rate indicates that the dominant phase-breaking mechanism in our 2D system is due to electron-electron interaction.