Assume in one response, Choice 1 is chosen. If the percentage, say 200% (2.0), in the response is entered into "Weight", it does not mean Choice 1 is 100% more preferred over Choice 2. It means there are 2 responses chose Choice 1. Just like the person who submitted that response voted Choice 1 twice. There is no comparison information about Choice 2 being entered.
Based on that understanding about what "Weight" does, the percentage information could enter the analysis by constructing the data like this:
1) Duplicate the response, but change the choice of the copy to the opposite choice, Choice 2 in this case.
2) Set a weight to the original response. For this example, it should be proportional to 200%.
3) Set a weight to the copied response. For this example, it should be proportional to 100%.
By such, we are creating a situation, in which the responses that choose Choice 1 are twice as many as the responses that choose Choice 2.
Notice, I said "proportional". Because we need to make sure the sum of two weights is a constant for every pair of responses that are created in this way. E.g. if the sum is 300%, it must be the same 300% for all the remaining pairs.
But, here, for Choice model, what does 200% preferred mean by a single person? One should either choose or not choose. If the data do not firmly represent choose or not choose, how to interpret the resulting model then?