No absolutely not, it does not weaken the fabric. This is from someone that has been tearing for 28 years it is great. I still tear all my large pieces for my quilts, my borders my backs and sometimes large blocks, no stretching, nor distortion, yes a little fraying, but It is always an exact measurment. I have found quilters that have only known cutting cannot stand the thought of tearing. The first thing I do when I get a piece of fabric home is straighten by tearing. I can't tell you how many times I have gotten a piece of fabric home where they have used a rotary cutter or scissors and it so off I lose over 6 inches., especially if it has a pattern. And the stores because they use rulers and rotary cutters think they are so exact, you are lucky if they give you 2 inches extra.
Just don't rippppppppppp, tear gently and slowly.