Split a list into sized chunks, but not counting items failing predicate
Brachylog, 37 bytes

hW&amp;t~c.k{↰₂ˢl}ᵐ;WxĖ∧.bhᵐ↰₂ᵐ∧.t↰₂ˢl≤W∧


Try it online!

I was pleasantly surprised to find that this - pretty much a restatement of the question - successfully terminates and produces correct output. 

Assumes the predicate is present as predicate 2 below this code. Outputs a list of lists ("chunks"), or false for an empty input. 

Explanation:

hW&amp;               % First input is W, the expected "weight" of each chunk
                  %  (i.e. the number of items passing predicate in each chunk)

t                 % Take the second input, the list of items
 ~c.              % Output is a partition of this list
    k{    }ᵐ      % For each partition (chunk) except the last, 
      ↰₂ˢ         %   Select the items in the chunk that pass the predicate
         l        %   Get the length of that
                  % (So now we have the list of the "weights" of each chunk)
            ;Wx   % Remove the input expected weight from this list, and 
               Ė  %  the result of this should be empty.
                  %  This verifies that the list of weights is either 
                  %  composed of all W-values, or is empty (when input is [0 0 0] for eg.)

    ∧.bhᵐ↰₂ᵐ      % And, the first element of each chunk (except the first) should
                  %  pass the predicate. This is another way of saying:
                  %  "Items failing the predicate are allocated to the earliest chunk"

    ∧.t↰₂ˢl≤W     % And, the final chunk (which we haven't constrained so far)
                  %  should have weight ≤ the input expected weight
                  %  This disallows putting everything in the final chunk and calling it a day!

    ∧             % (no further constraints on output)