That "blackberry tree" is likely white mulberry (Morus alba), imported from China in the 1600s for silkworms. Silkworms failed; the tree thrived. Red mulberry (Morus rubra) is native but less common. Paper mulberry (Broussonetia papyrifera) has similar leaves but orange spiky fruit.
Put a leaf edge in your mouth: Red mulberry = fuzzy underneath. White mulberry = smooth underneath.
Purdue Extension publication (linked) details full identification.
Fruitless Mulberry Trunk Splits: Structural Damage, No Cure
Distinguishing White vs. Yellow Peach Seeds
White Pine vs. Red Pine: Identification and Commercial Value
Best Tree Identification Field Guides for Eastern North America
Dwarf Red Banana Fruiting Timeline and Care
Red Mulberry (Morus rubra): Native Sweet Fruit for Wildlife and People
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