Tension in the air

My mom just bought some poupouri for her car and as I was filling the little pouch with all of the beads, I was reminded of tension. As I was tugging the pouch shut, I was exerting a force on the string that added to the tension in it. The combined vertical tension of the two strings was equal to the weight (massxgravity) of the pouch and the horizontal tension of the strings going in opposite directions were equal to each other once the pouch was pulled shut. However, while I was pulling the strings, the left side seemed longer than the right side, which I think means that I pulled with more force with my left hand than my right. But then, time is used for power, so maybe my left hand used more power?