This research paper looks at quantifying the effects heavier shoes has on running times. Blinded to the runners, the researchers placed lead weights into runners shoes (normal shoe weight, normal shoe weight +100gm and normal shoe weight +300gm) and then had them run on a treadmill and perform a 3km time trial. The data shows that energy costs of the runner increased by 1% for ever extra 100gm of weight.
It should be noted though, there is a lower threshold limit for shoe weight. Ie, having the lightest possible shoe doesn’t mean you will run the fastest. The cushioning of the shoe helps to absorb impact shock and therefore reduces energy expenditure. If you remove too much cushioning, energy expenditure will increase because that cushioning effect is greatly diminished.

Treadmill running with heavier shoes tied to slower race times