I have read answer by @John Rennie in regards to the size and density of black hole. In the last sentence he states that super supermassive black hole with the mass of 4.3 billion Suns would have a density equal to one i.e. the same density as water.
Does that mean that there is a limit to the size of black hole? (otherwise I should be able to swim in it). What am I missing here?
As stated in the answer you linked, the density of a black hole is defined by the ratio of its mass over the volume spanned by its Schwarzschild radius. That does not mean that there is actually uniformly distributed matter inside the Schwarzschild radius. All of the matter is packed very densely (in something with the characteristic length of the Planck scale) around the singularity ("classically" i.e. without quantum gravity, the density is zero everywhere but in the center, where it is infinite. This is why it is defined in the other way). You certainly can not swim in a supermassive black hole.
