Pass the updated value of aid from form using ajax

I’m a bit confused – why the two submit buttons? And you’re outputting the same id multiple times (inside a foreach loop), which will choke jQuery. Try the following, using classes:

$form = '';
foreach ( $results as $result ) {
    $value = esc_attr( $result->aid );
    $form .= '<form method="post" class="aid-form">';
        $form .= "<input name="aid" type="text" value="$value" />";
        $form .= "<input name="star5" class="star" type="submit" value="5" />";
    $form .= '</form>';
}

And then your jQuery:

$( document ).on( "submit", ".aid-form",
    function( e ) {
        e.preventDefault();
        var data = {
            action: "star",
            aid: $( this ).find( "input[name=aid]" ).val() // Get value of "aid" from current form submitting       
        };

        $.post(
            yes.ajaxurl,
            data,
            function( result ) {
                window.alert( result );
                $( "#myresult" ).html( result );
            },
            "json"
        );
    }
);