If the trailer starts to oscillate back and forth uncontrollably like an excited dog's tail, it's a major hazard. But if it just gives a little wag to one side and the other and then settles back into line, that's uncomfortable but not a huge safety problem. A hitch weight 10-15% of TT weight should keep the TT from being subject to oscillation (dangerous sway).
Did you say your sway bar came standard with the truck? Are we talking about the same thing, I wonder? Most of us are referring to an adjustable friction sway bar that attaches to both the truck hitch and the trailer tongue. Assuming you mean the same thing (and not some sway bar under the truck), then in addition to another friction bar (or an Equal-i-zer hitch), I'd look at the truck tires. Make sure they are inflated to max. Sometimes a tire's sidewalls can still squirm under load, though, so a lower profile tire might be worth considering. Just some random ideas to add to all the good stuff others have suggested.
