I'm adding ?show={COUNTRY CODE} to URL as a parameter. I managed to add it with the code below but can't remove it when you unselect the checkbox.
$.urlParam = function(name) {
  var results = new RegExp('[\?&]' + name + '=([^&#]*)').exec(window.location.href);
  if (results) {
    return results[1];
  } else {
    return 0;
  }
}
$('#uc').click(function() {
  var country = $(this).val();
  var site_url = $('body').data('site-url');
  var url = $('body').data('url');
  window.location.href = site_url + url + '?show=' + country;
});
if ($.urlParam('show') == $('#uc').val()) {
  $('#uc').attr('checked', true);
}<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<input type="checkbox" name="uc" id="uc" value="UK"> <label for="uc">Only UK</label> 
     
    