  In our setting enumeration amounts to generate all solutions of a problem
instance without duplicates. We address the problem of enumerating the models
of B-formulae. A B-formula is a propositional formula whose connectives are
taken from a fixed set B of Boolean connectives. Without imposing any specific
order to output the solutions, this task is solved. We completely classify the
complexity of this enumeration task for all possible sets of connectives B
imposing the orders of (1) non-decreasing weight, (2) non-increasing weight;
the weight of a model being the number of variables assigned to 1. We consider
also the weighted variants where a non-negative integer weight is assigned to
each variable and show that this add-on leads to more sophisticated enumeration
algorithms and even renders previously tractable cases intractable, contrarily
to the constraint setting. As a by-product we obtain complete complexity
classifications for the optimization problems known as Min-Ones and Max-Ones
which are in the B-formula setting two different tasks.
