A modified bathroom rug placed in front of the sink in the bathroom would be a better option as with the doormat you'd have people weighing in with their shoes, jackets, backpacks, bags, belts...
The bathroom rug would be great as that is where everyone's day starts and ends usually, when brushing teeth. A smart mirror could be used as the screen. Connected with the other mirrors in the household.
It's also a great way of standardizing measurements because you enter and exit the house at various times, with different levels of hydration. With bathroom check-ins, in the morning you'd have approximately the same level of hydration, while at night you'd get some sense of how much did you ate throughout the day.
Further down the line, it could be possible for a smart bathroom to block the user from using some of its functions if he doesn't reach his target goal for over a week. So something like block opening of the cabinet behind the mirror, possibly the hairdryer, definitely not the flushing :). You could even make the faucets unavailable until you get measured for the day to ensure commitment and consistency.
Somewhat similar to the idea I recently had for blocking credit card purchasing of clothes.