This is how Weekend Warriot works in my game. I'm writing about it in hopes of someone getting help using it.
When WW starts, in a few seconds I get 40 energy. There is no other sign of anything special happening energywise. When the 40 energies are used, I soon get a refill of 40. Refill seems to come when the energy clock has counted down from 3 minutes to around 50 seconds. It also seems to help if I click on something and see the "You don't have energy for this" screen. After a few seconds I get a refill.
The refills are of course not as useful as the actual "unlimited" energy, but I've noticed that the refills keep coming a lot longer than 10 minutes, more like 20 minutes. That is why I have stopped force closing in hope of to trigger the "unlimited" energy. I prefer having the 20 minutes of refills, because it makes WW less stressful to have more time.
The second unlimited energy works the same way. I'm using android phone.
Please tell if you have some useful tips for WW.