No, weighted averages take into account what you've decided to measure and how you've decided to weight it. If I take the weighted average of the volume of a cat from tip to tail, I haven't said much about the dietary requirements of the cat, although some information towards that may be gleaned. Being able to take a weighted average does not, at all, mean you've successfully measured everything. This is reification -- you've done math and confused the concrete outcome of the math as applying to your assumptions. Nothing in stats will correct your assumptions -- tools will gleefully let you lie to yourself with the absolute certainty of a math equation. Don't confuse "I did math!" for "I did it right!"It's statements like the one above that make me question whether you really understand what a weighted average is.
Weighted averages by definition does take into account EVERYTHING. That's why I'm very puzzled when you make statements like these. My average rounds to kill takes into account rounds 1 to infinity. Your chance to kill by round X only takes into account rounds 1 to X.
For example, if you look at your round two, the information contained is that the creature wasn't killed in round one and here are the odds it is killed in round two. In mine, all of the information is present -- both the odds it was killed in round one and the odds it was killed in round two. These are answering different questions, so missing information isn't necessarily a bad thing, but you need to really look at what you've decided to measure to see if it suits your assumptions. Doing math doesn't fix faulty assumptions.
And, so far, I'm unclear as to what your assumptions are -- you seem to think that because you've shown something that this means that another thing is less valid (the overkill fallacy, as you've termed it). This is like taking the weighted average of a the volume of a cat and declaring that you know it's dietary needs, though -- these things may correlate on some level, but they aren't causative in the way you've presented them. You haven't shown how your weighted average says anything at all about overkill.