The thumb rest on a saxophone is not intended to lift the instrument, but to keep your thumb in the right place. Lifting the sax with your thumb can lead to injuries on your thumb or arm. Your strap is there especially to carry the sax. With that right thumb, you can push the sax away a bit from your body. Or a lot, in case you want to show of a bit. Be careful not to put too much strain on your arm. I use that great new strap, the Saxholder, for protection against injuries.
