I have enjoyed this car ( the past 4 days ) save for one thing

The ride over slightly rough surfaces is fine.
But over uneven dips in the road the body heaves in a left right fashion
Is there anyway to tame this tendency ?
I am not carrying heavy loads. I weigh over 200,
No passengers , and a few hundred in items in truck / car
Tires are not high end ( car was bought used with 23000 miles )
Firestones
Tire psi is around 33 34

Do I need a sway bar?

Thank you