While Edgel3d's answer seems to produce the desired effect, it's not physically accurate (although, admitedly, having two separate groups of objects experiencing different gravity wouldn't be physically accurate anyway!!) - it's more like adding 'drag' or 'air resistance' to the objects so as to slow them. If you run the simulation for longer you'll find that the 'slowed' objects will reach a terminal velocity where they no longer accelerate as they would if the force was purely gravity.
To achieve a physically accurate different force of gravity you can disable the 'world' gravity and implement the equivalent force using a Force field. Since Fields only affect objects on the same render layer you can easily control which objects are affected by which force.
Firstly, disable gravity by either disabling it on the Gravity properties panel or by changing the Gravity Field Weight to zero.
To mimic the gravity, add a Force field (Add, Force Field, Force). The Force pushes any objects away from wherever you place it - position the Force above all objects so that it acts to push objects 'down' (as would have occurred with 'normal' gravity). In the Physics properties panel set the force Shape to 'Plane', set the Strength to '225' (this seems to mimic the standard gravity of 9.82) and ensure the Falloff Power is set to 0 (this will result in no falloff - so the force acts the same regardless of distance). Since the Shape is a Plane rather than a Point, the force will always act in the Z direction of the Field (ie, 'down').
Duplicate the Force (Shift-D) and right-click to leave it in the same place as the original. Press M to move it to another render layer and select the render layer to use for the altered gravity. Amend the Strength of the Force on the second render layer to whatever 'altered' gravity you desire. Move all objects that want to have the adjusted gravity onto the second render layer. Select both render layers by holding Shift and clicking the render layers in the toolbar.
You should now find that the objects obey the differing gravity depending on which render layer they are placed.
Blend file attached