Well, it matters if you care about measuring your fat loss. Measuring fat loss by tracking weight is less accurate, because muscle is heavier than fat, if you are exercising to lose fat you may get heavier due to increased muscle mass, even though you are thinner, i.e. carrying less fat. There are other factors that affect your weight, such as water retention. As for why to measure at the hip, well, there isn't much muscle around that area compared to say your thigh, so the size of the muscle is not affecting the measurement output so much, meaning you are measuring fat loss, rather than fat+muscle loss/gain. (Muscle loss is generally not a good thing, it's very important to our health).
Personally I think we need a way to measure our health rather than tracking metrics that can encourage unhealthy relationships with our bodies. Ideally we would be able to quickly assess how close we are to a healthy level of body fat, lean muscle mass, be it is too high or too low. Measuring how heavy / big you are feeds into "weight status" and "thigh gap" fixation. In a less-imperfect world we'd be competitive about how healthy we are, rather than silly and often unhealthy things like thinness, and weight.
If we're talking about fitness goals, generally, weight is actually a fairly poor indicator of progress. Someone can be 200 lb and another person can be 180 lb, and both can be the same height; yet the 200lb person might be stronger or more athletic, while the 180lb person could have very little muscle mass and a much higher body fat %.
Stated in another way, it's entirely possible that a person can gain weight and lose fat -- or even lose weight and accumulate fat.
The size of various parts of your body is a much better indicator compared to measuring weight (measuring one overall size isn't a great help either), although still not the best. Measuring body fat % would be best, but unfortunately, it's not very easy to do so -- at least not without special tools.
Personally I think we need a way to measure our health rather than tracking metrics that can encourage unhealthy relationships with our bodies. Ideally we would be able to quickly assess how close we are to a healthy level of body fat, lean muscle mass, be it is too high or too low. Measuring how heavy / big you are feeds into "weight status" and "thigh gap" fixation. In a less-imperfect world we'd be competitive about how healthy we are, rather than silly and often unhealthy things like thinness, and weight.