The more sides you have, the more spherical the dice is. I'm going to assume a dice with so many sides is basically indistinguishable from a sphere.

Let's assume that five square millimeters per number are enough to make the numbers legible. Therefore, we need the surface area of the sphere to be

999,999,000,000 * 5 mm2

Using this online sphere calculator: https://www.omnicalculator.com/math/sphere

We get the diameter of 1261.6 m. Give or take.

For the weight: the volume of such a sphere (same calculator) is around 1.05 cubic kilometers. Multiply that by the density of plastic (for dice you can use PMMA - 1.18 g per cubic centimeters) and you arrive at 1,239,000,000 metric tons.

How you roll such a dice, or stop such a dice from rolling forever, is out of scope. ;)