I just figured out your question by doing the following:
1) get a bathroom scale, weigh yourself and write down the weight
2) do a close grip pushup on the scale reading off what it says. This number got larger as I got closer to the scale because of the shift in center of gravity towards your hands on the way down.
3) figure out the percentage of how much weight you're lifting on a pushup.
(step 2 weight / step 1 weight) x 100 =
percentage of BW lifted on a pushup
my percentage was 66% of BW at the top and 77% at the bottom.
When you add weights, try and position them directly over your scapula/towards your head so that their weight has a greater load on your arms/chest/shoulders as opposed to on your feet. I would think this is also safer as it would prevent the weight from sagging your hips down to the floor and straining the back.
You should post your % results that you got using this method, and we can see if they're similar to mine.