JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="http://code.jquery.com/ui/1.8.22/themes/base/jquery-ui.css">
Start Date: <input type="text" id="startdatepicker"/><br />
End Date: <input type="text" id="enddatepicker"/><br />

JavaScript

$(document).ready(function() {
    // Get current date
    var now = new Date();
    // Get the day, 0 is Sunday and 6 is Saturday
    var day = now.getDay();
    
    // How many days to this sunday
    var daysToSunday;
    if (day == 0) {
        // Sunday is now
        daysToSunday = 0;
    } else {
        daysToSunday = 7 - day;
    }
    
    // Days to next saturday is simple:
    var daysToNextSaturday = daysToSunday + 6;
    
    // See defaultDate option,
    // http://jqueryui.com/demos/datepicker/#option-defaultDate
    $("#startdatepicker").datepicker({
        dateFormat: 'dd/mm',
        defaultDate: daysToSunday
    });
    $("#enddatepicker").datepicker({
        dateFormat: 'yy-mm-dd',
        defaultDate: daysToNextSaturday
    });
});