JSFiddle - React, Tailwind, and code Playground

HTML

<table id="dlList" cellspacing="0" style="width:100%;border-collapse:collapse;">
        <tbody>
            <tr>
                <td>
                    <table width="100%" cellpadding="2" cellspacing="0" border="0">
                        <tbody>
                            <tr class="table-headers">
                                <td width="300" align="center">Description</td>
                                <td width="80" align="left">
                                    <span id="dlList_lblSortHeaderx">Sort</span>
                                </td>
                                <td width="100"></td>
                            </tr>
                            <tr>
                                <td colspan="6">
                                    <br>
                                </td>
                            </tr>
                        </tbody>
                    </table>
                </td>
            </tr>
            <tr>
                <td class="padding-top padding-bottom border-bottom" style="color:Black;background-color:White;">
                    <table id="dlList_Table1_0" style="width:100%;">
                        <tbody>
                            <tr id="dlList_rwGroupHeading_0">
                                <td id="dlList_Tablecell1_0" class="td9Header" align="center" colspan="6">
                                    <input type="text" />
                                </td>
                            </tr>
                            <tr id="dlList_rwCategoryHeading_0" class="margin-botom">
                                <td id="dlList_Tablecell6_0" class="td9Header padding-bottom padding-top" align="center" colspan="6" style="background-color:#EBEBEB;">
                                    <span id="dlList_lblCategoryHeadingx_0" style="font-size: 20px; font-weight: bold;">Heading</span>
                                </td>
                            </tr>
                            <tr id="dlList_rwItem_0">
...

JavaScript

$(document).ready(function(){
  $(".up,.down").click(function(){
    var row = $(this).parents("#dlList > tbody > tr").first();
    if ($(this).is(".up")) {
        row.insertBefore(row.prev());
    } else {
        row.insertAfter(row.next());
    }
  });
});