Technically, when we talk about 'weighting' we usually mean some system that takes all the options into account, but factors the weights together to make a choice.

For example, if you could choose any of the options, but are more likely to choose the high-scoring ones, this is technically known as 'fitness proportional selection' or 'roulette wheel selection' in some circles, but is often just called 'weighted random': https://en.wikipedia.org/wiki/Fitness_proportionate_selection

But if you're just picking the highest-scoring option each time, that's not really a 'weight'. It's basically a score which yields a rank. The simple act of making a choice based on a score or ranking is known as a utility system, based on the game theory concept of utility as being an abstract score for how important or useful something is. Some utility systems will actually use roulette-wheel selection rather than just picking the top-scoring action.