the empty curly brackets are for the true condition.
so you are saying if Quantity of items Where RecID is Greater Than or Equal to $eCart1->DisplayInfo("ID") : Do Nothing
Else: Show the checkbook.
perhaps you what to be using less than:
<?php if ($eCart1->ConditionalTotal("Quantity", "RecID", "" . $eCart1->DisplayInfo("ID") . "") < 1) {
?>
<input type="checkbox" value="<?php echo $eCart1->DisplayInfo("ID"); ?>" name="eCart1_Delete_<?php echo $eCart1->DisplayInfo("WAUID"); ?>" />
<?php } ?>