This is not a great design.
The exact weight of concrete required to keep this from tipping over depends on how far out the load is suspended. If we assume you are hanging the load 24” from the post (18” from the edge of the concrete) you will need about 3X the weight of the load: 600 lbs of concrete. In a 12” diameter cylinder you would need the concrete to be more than 5 feet tall (assuming your concrete weighs 150 lbs/cu-ft). If you went up to a 24” diameter base the situation is a lot better because you have more concrete and more leverage, but I am not sure if the post would really be stable in such a large block of concrete without reinforcement.
There is also the issue of the serious amount of bending you are putting on a 4x4. This is not an axial load.
I would recommend another design. Either put supports on both sides (like a swing set) or stabilize the post with guy-wires into the ground.