John,
as the others have said, it looks like Blanche (aka Bianci, Lemon, White Marseilles). And yes, the leaves of many varietals become smaller as the tree matures. Here is what Givan says about it:
"An old, reliable variety. Medium to large greenish-yellow figs with white pulp. Turbinate with or without a short neck. Leaf: base subcordate; 3-5 lobes; margins crenate. It has a small, but open eye and will sour if left too long on the plant. Also subject to splitting, if watered too much when fruit is ripening. Well-adapted in the South where, known as Lemon, it is an heirloom variety. Slow growing. Condit calls it Blanche. (See the discussion of this name in the Introduction.) Hardy. It has a spritely sweet flavor and nutty texture (from the "seeds"). Good fresh, better dried and superb stewed."
Good luck and enjoy!