I assume you have a helical spring (like a spiral staircase). If the turns of the spring are touching each other when the spring is unloaded, the spring might well need a small load to separate the turns. A greater load will then produce a gap between the turns, so the spring will start to gain an extension.
It's easy to understand what's going on once you realise that the main mechanism involved in stretching a spring is twisting (torsion) of the wire of the spring about the central axis of the wire (I don't mean the central axis of the spring). Suppose that anchoring the top end of the spring and pulling the bottom end of the spring produces an anticlockwise twist in the wire (seen from its bottom end). But if the spring has a built-in a clockwise twist in the wire, this has to be overcome before the turns separate and the spring starts to stretch.