To fly above ground effect, you need thrust equal to the weight of the aircraft (or slightly more, as you want to climb).
Ground effect doesn't hold aircraft down, it just makes it easier to fly when they are close to the ground. The exact amount varies quite widely depending on exactly how close the wing/rotor is to the ground. For a plane or helicopter it may only be 10% extra lift, but a vehicle designed to maximise ground effect (like a hovercraft) can fly with vastly less power than would be required to fly without ground effect.
Ground effect is particularly noticeable if you hover a model helicopter inverted over a smooth surface. As it descends towards the floor, it looks as if it lands in a big soft cushion - decelerating and bobbing around at about half to a third of rotor diameter. You can hover without the constant adjustments in collective pitch that are normally required, and need to drastically reduce thrust to go lower. When you're half an inch or less off the floor, it's probably only using 10-20% of the pitch required for normal hovering, and there's a self-levelling effect so it's much easier than it looks!
For a typical FPV quadcopter with 5" props on top of the motors, you almost can't feel ground effect if you put the battery under the frame. With the battery on top you can feel a noticeable cushion and you can find a throttle setting that holds the quad off the ground but won't climb out of ground effect. I'd estimate that it's flying at about 80-90% of normal power.
While the power may be reduced, it can be harder to hold a multi-rotor or helicopter in place when in ground effect. The bubble of higher pressure tries to escape out from underneath the aircraft, pushing it in the opposite direction.
A general rule of thumb is that the reduction in power due to ground effect starts to be noticeable when the altitude is less than around half or a third of the wing span or rotor diameter. The 'air bubble' effect on position holding while hovering is noticeable one or two diameters above the ground. Both tail off gradually so there's no hard limit.
* What is ground effect?
* How high does the ground effect last?
* Does ground effect scale 1:1 with wingspan?
and lots more, over at the Aviation stack-exchange.
Also this excellent academic paper:
Characterization of the Aerodynamic Ground Effect and Its Influence in Multirotor Control