Given a set of constraints F and a user-defined weight function W on the assignment space, the problem of constrained sampling is to sample satisfying assignments of F conditioned on W. Constrained sampling is a fundamental problem with applications in probabilistic reasoning, synthesis, software and hardware testing. In addition to constrained sampling, we are often interested in projected sampling over X from Σ_1^1 formulas, i.e., G(X) := ∃Y F (X, Y) for some F; typically the set of variables Y are introduced as auxiliary variables during encoding of constraints to F. To tackle these problems, we present a novel technique, called WAPS, which proceeds by sampling in linear time over the size of the formula’s d-DNNF, a well studied compiled form. WAPS achieves a geometric speedup of 296x over state-of-the-art weighted and projected sampler WeightGen and its runtime is agnostic to the underlying weight distribution.