A good scale which uses impedance to give a reasonably accurate measure of body fat % is fairly cheap nowadays, fyi. I got mine for about £25 in the UK. It's accurate enough to tell you whether your fat is dropping overall, week after week - just make sure you measure at the same time each day (ideally, just after waking up, before having breakfast).
Also, the end result is fat loss, not weight. Which is why I think weight is not the best metric, but performance in physical tasks. (As most people can't get their bodyfat percentage checked regularly, and performing various physical tasks is what allows you to keep or increase muscle mass while losing body fat.)