Cyp half life is more like 8 days... But think about half life:
Say you took only one injection of 100mg. One week later there's 50mg left. Another week there's 25mg left. ANOTHER week later there's 12.5mg left... then 6.25mg... then 3.125...
Now let's look at weekly injections:
You inject 200mg on Sunday. A week later there's ~100mg still left/available.
You inject another 200mg on that day. Now there's a total of 300mg in your system.
One week later 100mg of the last injection is still available and ~50mg of the injection before that one... so there's a total of 150mg left/available.
One week later 100mg of the last injection is available, ~50mg of the one before that, ~25mg of that first injection. Now there's 175mg left/available. Inject another 200mg, for a total of 375mg in your system.
One week later... there's a pattern here. 1/2 of last week's injection amount, 1/2 of what was left from the injection before that, 1/2 of what was left from the one before that, etc... so you've got, ahhh... fucking math... a total of 100+50+25+12.5. See how that's adding up?
Eventually there's a point to where it evens out and you stay at a peak of ~X amount, and a valley of ~Y amount. The longer duration of time between injections, the greater difference between the peaks and valleys.
The idea behind injecting every 3.5 days is to minimize the peaks and valleys of Test levels.
I'm on TRT & my natural production is totally shutdown. I'm taking 200mg/wk, divided into two doses 3.5 days apart. It's kept the peaks/valleys pretty decent, but I can feel the valley. I'm a little more irritable and aggressive then. During the peak I'm happier and hornier.
I've also had blood tests during the peaks and valleys. Even at 3.5 days between injections, my Test levels fluctuate ~350ng/dl up/down.
I haven't had my coffee yet... hope any of that makes sense