I am seeking to ping a server from my webpage (also I own the server it's on)

Any suggestions on how to ping it and return a value of "Online", "Heavy Loaded" or "Offline" based on the returned values?

You can do a call to return a value from a specific page from the other server.

PHP Code:

<?php
  
  $handle = @fopen('http://www.domain.com/check_status.php', 'r');
  
  $status = (int)@fread($handle, 1024);
  
  
  if ($status == 1)
  {
    // Server is online
  }
  else
  {
    // Server is offline
  }
  
  @fclose($handle);

There is a class written you can use to measure the server load in a percentage at http://www.phpclasses.org/browse/package/3109.html

Doing this, you could return a value of 2 or something if the load is above a threshold you set.