Yes, the laws of physics limit the radii of planets and stars (we talk about the radius here because mass is heft, while size means dimensions).
No, there could not be a planet as large as the Sun, using the standard definition of planet (that is, not calling a stellar object a planet just because it orbits another star).
No, there could not be a star as large as our solar system. The largest stars yet observed have radii which may approach that of the orbit of Saturn, around 9-10 AU; in contrast, the radius of our solar system as a whole is more like 100,000 AU.
Such mega-massive stars sit just beneath the Eddington limit, which is the point at which outward radiation pressure exceeds inward gravitational force. Beyond this, they could not cohere as objects — this is what happens when stars go poof.
Stars like this (St2-18, say, or UY Scuti) are extremely low-density; their masses do not scale up with their sizes in the way you might intuitively suppose. If the Sun is a solid baseball, then these guys are gas-filled hot air balloons in comparison.
They’re big puffballs of radiation, shining with extreme luminosity but barely holding together gravitationally.
Models are being refined as scientists gather and analyze more data, but we think this maximum size is somewhere near 2,000 R☉. Two thousand times the radius of the Sun is intimidating enough! But poke it with a toothpick and it bursts (so to speak).
UY Scuti has nearly 2K times the girth of the Sun, but that is still nowhere near the radius of the whole solar system.
The radius of a planet is constrained by the fact that, the more mass you add, the more gravitational compression you get scrunching the thing down smaller, or at least preventing it from expanding into something larger. (So, more mass = bigger planet only up to a point.)
Eventually, if you add enough mass, this compression will ignite fusion and you get a star instead.
Jupiter is fairly typical in radius for a really big gas giant. We have observed some which are larger — often 1.5–2 RJ, and in rare extreme cases perhaps as large as 6 RJ. But when you get that big, it’s possible you’re looking at a brown dwarf. Gas giants don’t get a whole lot bigger than Jupiter unless they’re quite hot (i.e., in close orbit of a star). Otherwise 2RJ could mean something like twenty times Jupiter’s mass, and that’s inviting deuterium fusion.
You can have rocky planets as large as a few Earth radii. But if you doubled the mass of Earth, you would only increase its radius by around 20–30%. Here again, gravitational compression is a limiting factor.
And they call gravity the weakest force! Well, it is, but it utterly dominates at the scale of everyday objects, including suns and worlds.
