I'm surprised that this wasn't already done - could you save fuel if you knew you had a lower take off weight? Or maybe weigh the whole plane before take off?

I'm surprised that this wasn't already done - could you save fuel if you knew you had a lower take off weight? Or maybe weigh the whole plane before take off? I find it amusing that weight is somehow some precious value, though. If someone is embarassed about being fat I mean, everyone around them can see that.