Everything I have read keeps bringing me back to something in the Linden family or a Swamp Cottonwood. I’ve never noticed it blooming or bearing fruit, but we just really started noticing it last year. This year, I’ve determined that I will watch it more closely this year!

Maybe a species in the basswood aka linden (Tilia) genus? Check it out if you have a match in the genus. Best wishes! http://floridata.com/Plants/Tiliaceae/Tilia%20americana/798 http://plants.usda.gov/plantguide/pdf/cs_tiama.pdf

There were 2 other pictures of the full tree and a close-up of the edges but neither uploaded for some reason. If anyone has any ideas, please let me know!