The Shardblade is connected with his punishment somehow, he's specifically not allowed to give it up, even if somebody orders him to give it up, that suggests it's somehow connected with being Truthless, but there's one line from Taravangian about Szeth having been given the Blade by his people, which suggests that carrying it is actually part of his punishment, rather then the cause of it. OF course T. could have been wrong, but Szeth didn't correct him.