Thank you all for good advice!
Also thanks to Steyr factory for prompt reply and excellent customer service!
I collected the info that I found regarding this issue (see below).
I followed Procedure 1 and reached 1.stage=380g and 2.stage =140g.
I am not making any recommendations myself, just telling what worked for me.
Carl
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EVO 10 Trigger
Trigger stop (nr 1)
Too fine adjustment of the trigger stop may cause inconsistent trigger weight and release. (Evo user manual)
Make sure your over travel has clearance and is not affecting the second stage weight. (brent375hh)
Check that the trigger stop screw is not contacting the frame at release (page 31 manual- screw 1).
Wind screw 1 anti-clockwise 1 turn and re- check the trigger. (David M)
First stage:
It will help if you shorten the first stage travel. The more travel it has, that spring is still compressing into the second stage somewhat. (brent375hh)
Sear screw (nr 5 red paint seal - the Don´t touch screw):
Cock the gun and turn it in slowly until it releases. Then back out 60-70 degrees. (brent375hh)
Also, have you touched screw 5 (sear engagement) normally factory set. If this is set as too small an
engagement, it will require a heavy 2nd stage weight to retain engagement. (David M)
New spring:
If none of that works, yes I would procure a new spring. When you have the sear out, I grease its contact edges with moly grease. My view is that it keeps sear wear down and makes the trigger just work against springs, and not friction. (brent375hh)
Procedure 1 (David M):
Total reset....
Turn scew 1 anticlockwise to allow trigger after travel.
turn screw 3 to allow 3-5mm travel at the centre of trigger blade.
turn screw 2 to give approx. 300g of first stage weight.
turn screw 4 to give approx. 200g second stage weight.
These are the rough settings.
Now to adjust the sear. (the don't touch screw)
you need 1/8 to 1/2 screw engagement of the sear. The amount of engagement also acts like a second stage travel.
1/8 of a turn will be a break like glass setting and a 1/2 turn a slight roll off.
The lighter you set the second stage weight (screw 4) the more sear engagement you need for reliable operation.
With the pistol cocked slowly turn 5 in until the pistol fires (sear releases) this is the break point. Note the screw head slot angle.
Now back off screw 5 a 1/4 to 1/3 of a turn, re-cock and try the trigger feel. Feel for the second stage travel.
Adjust a very small amount as required but not less than 1/8 turn from break point. (Sear set)
Slowly wind in the trigger stop (screw 1) until the pistol won't fire, then back off 1/2 turn. (Over travel set)
Adjust overall trigger travel to your liking.(screw 3). (trigger travel set)
Now fine tune the second stage weight for your feel but not less than 100g. (150- 200g is good).
Adjust the first stage weight to lift +500g.
If feel and weight is right ,lock screw 5 with nail polish or a small dab of super glue.
Procedure 2 ( gimgim) :
First I fully unscrewed (I), (II), and (III). This should get the longest first stage with the minimum weight possible.
Verified than the pistol was still firing like if it didn't have a first stage, and without the tip of the screw (III) touching anything.
At that point, the only possibility seemed to be the sear not being engaged well enough and the pistol firing not because the tip of (III) pushes the lever, but because the hold at the opposite side of it is lifted.
I unscrewed (V), the screw Steyr says shouldn't be adjusted, ever 
by a tiny fraction (red paint seal was still there, but it wasn't securing the screw) and then adjusted second stage weight (IV), and the first stage length and weight.