For each segment of the take-off climb there is a minimum climb gradient which must be achievable. Increasing take-off mass decreases the achievable climb gradient. So at some value of mass the aeroplane is just able to achieve the required climb gradient. If you increase the mass more, the maximum achieveable climb gradient will be less than the specified legal minimum.
The Climb Limited Take-off Mass (sometimes called the WAT limit) is the maximum mass at which an aeroplane can acheive the minimum legal climb gradient.
Because the required climb gradients are specified as still air gradients, headwinds and tailwinds will not affect the Climb Limited Take-off Mass. But they will affect the actual gradient that can be achieved.
During the take-off climb all obstacles within the obstacle domain must be cleared by at least a specified minimum margin. This margin is equal to the screen height.
As mass increases, the achieveble climb gradient decreases. This reduces the height that the aircraft will achieve at each point along the net flight path. This in turn will reduce the amount by which it will clear each obstacle.
The Obstacle Limited Take-off Mass is the maximum mass at which an aeroplane can clear the most demanding obstacle by the required margin.
Obstacle clearance is determined by the actual climb gradient. Actual climb gradient is affected by headwinds and tailwinds. So the Obstacle Limited Take-off mass is increased by headwinds and decreased by tailwinds.