Area charts differ from line charts though in that they emphasize the cumulative integral under the line. In your weight example, in general the total of your weights on each day multiplied by the number of days is not a meaningful statistic (except perhaps to the operator of the elevator in your building who is tracking cumulative strain on the support cables). An area chart makes sense if the product of the x-axis and y-axis units make sense.
Data continuity is a secondary concern; there's no reason not to have a stepped area chart, which is the union of a set of adjacent bars representing discrete measurements. And sleep hours per day do accumulate nicely over time, so an area-emphasizing plot does make sense (sleep hours per day * days = sleep hours). It lets you look at two parts of the chart and assess 'did I get more sleep in this period or that period'.
Data continuity is a secondary concern; there's no reason not to have a stepped area chart, which is the union of a set of adjacent bars representing discrete measurements. And sleep hours per day do accumulate nicely over time, so an area-emphasizing plot does make sense (sleep hours per day * days = sleep hours). It lets you look at two parts of the chart and assess 'did I get more sleep in this period or that period'.