When Evolution Sage is in play, it proliferates my board every time a land is dropped. When I drop Blast Zone, it enters with 1 counter on it and then triggers the Sage. So after that the Blast Zone should have 2 counters, right?
Yes, it does. Blast Zone's ability modifies how it comes into play, so it's a replacement effect, and not a trigger ability like Evolution Sage's. It doesn't use the stack, and when Evolution Sage's ability resolves, it will have a counter you can proliferate.
If Blast Zone's ability would have read
When Blast Zone enters the battlefield, put a charge counter on it.
you would have to choose which ability triggered first, because you control both abilities; if you'd then choose Blast Zone's ability, Evolution Sage's ability would resolve before Blast Zone's and it would not receive an extra charge counter. But again, that is not the case.
Only if you choose to.
Glorfindel's answer is great, but misses this important point. From the reminder text on Evolution Sage, what proliferate actually does is:
Choose any number of permanents and/or players, then give each another counter of each kind already there.
So it's up to you if you want to choose Blast Zone. You could not choose it, in which case it'll still only have one counter. You could even choose your opponent's Blast Zone, if he has one on the board, to mess up opponent's math.