In the limelight: the center of attention. The phrase refers to a type of lamp that was previously used in theatrical stage lighting.
Think about when you have seen a moth or a fly drawn to a lamp or light. What happens if you turn on a second lamp in the room? Where do the bugs go? To draw attention from someone in the limelight to yourself is very similar to this analogy with the bugs. You can dampen their light by shining too brightly yourself at the wrong time.