You have one. It's know as your air conditioner. It's oversized if it's cooling and the humidity is still high, or you have a massive source of humidity that is seeping into the house. One of the most common complaints with an oversized system is higher humidity and lower temps. The system cools faster than the humidity is removed. Any chance your house is on a crawlspace?
When you get ready to replace your system, consider a two speed system. They don't require an upgraded ECM fan unit for the indoor unit. If the thermostat determines that high speed isn't required, it will run on the lower speed setting which would help dehumidify. My system is fully communicating, variable speed, which is nice because the indoor fan will run at a speed to meet what the outdoor unit is doing. Word of warning, this system is EXPENSIVE but impressive.
One more note: The Ecobee and other "smart" thermostats can undershoot the set temp to control humidity. I had to research it a bit but they have a setting to overcool to reduce humidity.
https://support.ecobee.com/s/articles/How-to-use-AC-Overcool-Max-to-reduce-humidity
https://support.google.com/googlenest/answer/9294957?hl=en
I'm gonna back up just a bit here. When is the last time your system was inspected and serviced? I question if you don't have a partially dry coil situation where only part of the coil is at the proper temp. I'd have someone check for blockage of the fins on the evaporator. You might just need a good cleaning. If the system charge has been adjusted over the years it will likely need checked after the coil cleaning. I'd want to make sure the indoor and outdoor coils are as clean as possible. If the coils are clean and the charge is correct, then I'd look at the thermostat. Older stats have a pretty wide temperature swing for on/off. Modern stats have a tighter swing variation and are often "learning" where they do better at keeping the indoor comfortable. Another benefit of a modern stat is the ability to use remote room sensors. If your bedroom tends to be a little warmer, you can set the stat to ignore the built in sensor and use the remote sensor in the warmer room for temperature and, if I'm not mistaken, humidity.
BTW, I'm working towards "influencer" status here.