How about using an accelerometer to measure the time taken to drop an iPhone from a known height. Then apply the tape to the object that you need to weigh on the iPhone and drop it from the same height. Using some fairly simple equations, you can determine the difference in speed of the end using the known gravitational acceleration and, therefore, the difference in weight. Subtract the weight of the iPhone and hey presto, you probably have the least accurate weighing device in the world (but without any additional equipment).
Edit
As indicated by Seth. The foregoing clearly does not work, since objects will accelerate at the same speed and, therefore, have the same final speed (different from any minimal effect of air resistance). To measure weight, it is necessary to calculate the force that the object hits the ground, which can then be used to calculate the weight (using F = ma). One way to achieve this (although not necessarily realistic) would be to have uniformly compressible planting material, where you can measure the distance that it compresses. The force that only one iPhone will use on the material is known as both m and a, and, as such, can be used to generate the force created by the combined iPhone and object.
As for the material that can be used to remove iphone, any suggestions?
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