https://plot.ly/javascript/bar-charts/#customizing-individual-bar-widths
Take a look at that link from the plotly documentation. It shows you how to create bars of varying width. If you want the date on the x-axis, simply pass date values as your x-parameter. Plotly automatically recognizes and handles it as a date.
If you do use time for your x-axis, you need to supply the width values in milliseconds.
Which chart widget are you using?