Looks like hackberry to me as well. Birds like the berries they produce but other than that pretty worthless from a wildlife perspective. The wood is very stringy and a low grade timber. The heart wood is a grey or almost purple color while the sap wood is nearly white. Grows on my place in what they call brackish soil (sandy/rocky) and damp. I have them in the same places I have my black walnut for the most part. If you have something nice next to one of these - cut down the hackberry!
I have quite a few hackberrys on my place, mine make excellent trees for stands cause they are large and very open canopies. Problem is they attract these lil almost gnat like bugs that bite the hell outta you!