Chazal explain that those who would bear the ark of the covenant were actually carried by it, rather than carrying it.
The Noam Elimelech offers another explanation of how this passuk relates to the Tzaddik:
When a Tzaddik starts on his journey towards HaShem, people speak out against him and cause him great difficulty. He doesn't pay them any heed however and continues pushing forward. These tests from those who challenge him actually propel him along on his way, the Noam Elimelech explains, and quicken his rise to greatness. (Each test in which he remains silent and ignores their taunting allows him tremendous spiritual growth.) When he finally becomes a true Tzaddik, he then returns the favor by awakening them [those who troubled him] to do true teshuvah and in this way, the Tzaddik who is referred to as the holy ark, actually carries those who at first appeared to carry him.