Add an id to your to your checkbox. It will look something like this, it is important that the id is after the variable as shown below.
[checkbox variable id:disablethis "variable"]
This will put the id "disablethis" on the span tag that surrounds your checkbox (input) that you are trying to disable. Then we can simply find that span and disable all of the inputs within it like so. Put this at the bottom of your form/page.
<script>
$("#disablethis :input").attr("disabled", true);
</script>