When your arm is straight, the angle of pull of the biceps is very weak. Almost all the force of the flexor muscles is directed to pulling the forearms into the upper arms, and only a small amount of residual force is used for rotating the forearm. However, as the forearm moves closer to the horizontal position, the angle of pull changes dramatically.
When the angle of pull is 90 degrees (when your forearm is close to the parallel position), the entire biceps muscle is being used to lift the forearm and the weights. At this time there is no or very little stabilization force (forces that pull into the elbow).
Because of this you are much stronger when your arms approach the 90-degree angle, and the weight that seemed heavy when your arms were straight now appears to be quite light. Thus, for maximum development of the muscle through the full range of motion, you should work it in the straight-arm and bent-arm variants.