To configure the weight parameters thru the BigML API, please click here. To do it thru the BigML Dashboard, in the dataset view, first choose CONFIGURE MODEL or CONFIGURE ENSEMBLE from the configure option menu, depending on what you want to build (an ensemble in this case):
In the ensemble configuration panel, you may set the weight options under the Weights dropdown:
It is worth mentioning that the weight field is valid for both regression and classification models and ensembles. In classification models and ensembles, you can combine it with balance objective or objective weights. If balance objective is chosen then BigML automatically balances all the classes evenly. When using Objective weights you are setting a specific weight for each class in classification models. If a class is not listed in the objective weights, it is assumed to have a weight of one. Weights of zero are valid as long as there are some positive valued weights.
Furthermore, you can read this blog post to learn how to correctly weigh fields of your datasets to tune the results of your model.