You can't really settle on a probability value unless you specify more precisely the procedure used to extract balls from the urn. Even in the case where the balls have equal weight, if you were allowed to peek into the urn and select a ball of the color of your liking, then the odds would not be 1:1 (you could always extract the blue ball, for example). Similarly, imagine a case where instead of having two ball of the same size you have a large cube and a tiny cylinder, but extraction from the urn is performed by another person that decides which one to extract depending on the flip of a fair coin. Then you could expect the probabilities to be 50% for the cube and 50% for the cylinder.
The urn model in which balls are considered equally likely to be extracted is nothing more than what the name says: a model. That is, an idealized description of some phenomenon. It may or may not be a useful representation of an aspect of the world depending on the context. For example, even the simple model of a coin flip which assigns a probability of 50% to heads and 50% to tail is a simplification that hides a lot of complicated physics, but which nevertheless is a good approximation to our day to day experience. See the paper "Dynamical bias in the coin toss" by Persi Diaconis and others (https://statweb.stanford.edu/~susan/papers/headswithJ.pdf).
