https://www.ecfr.gov/current/title-14/chapter-I/subchapter-F...
>any balloon that is moored to the surface of the earth or an object thereon and that has a diameter of more than 6 feet or a gas capacity of more than 115 cubic feet.
And the regulations on tethered balloons end up being even stricter than letting them go.
Some quick math tells me that you can lift approximately a kilogram of mass per cubic meter (at sea level, anyway). If your balloon's full weight is a half of a kilogram, you'd only need about a large beach ball filled with hydrogen to lift it. That seems like something that would be attainable for an outdoor DIY electrolysis setup.