You can rest assured that balsa trees are not invading Tennessee (at least not and living to tell about it)! Balsa trees are tropical trees that are hardy to around zone 10. They'd have to be grown in a heated greenhouse to survive here.

It appears that you have one of those nasty paulownias growing by your deck. They are very invasive (environmentally damaging) in Tennessee. The TN-EPPC rates them as a Severe Environmental Threat. Unfortunately, there are disreputable businesses pushing this scourge and putting out a lot of false info to get people to buy paulownia tees (seedlings and cuttings) from them, but they should be avoided like the plague.

If that were my tree, it would be gone at my very earliest convenience. There are plenty of much better alternatives.

There are several varieties of Pawlownia but none worth keeping , all things considered.