Heavy bicentennial quarter (6,05 gram)

This coin show up loose in a bag with other silvercoins.
Among them also half dollar and dollar (bicentennial). Most likely set open.
Both of them have normal weight.

However this weight 6,04-6,05 gram. 
Reading one place that +/-0.19 gram within normal range. If i get the coin tested and confirmed 0.400 silver. Any extra value?

First of all if your coin weighs 6.04 g that would be 5% above nominal weight (silver coin) or 6.5% above nominal weight (CuNi coin).  Typical variation on weight for these coins is +/- 2% (+/- 4% extreme).  Be that as it may, a Cu-Ni coin in that condition is worth $0.50 - $1.00.  A silver coin in that condition today is worth $5.29 in melt value alone so obviously extra value. It's easy to tell which regardless of weight. Look at the edge.  If you see copper on the edge it's a CuNi coin.

If it is a set with the half and dollar they also would be the same composition as the quarter. Look at their edges also. The S mintmark proves it is from a Proof or Uncirculated Mint Set. 

Forget to mentioned. But have looked at edge on all 3, and they are all silver.

That's good. Lucky you.  You can see values here. With the high price of silver the melt value today may exceed the values listed.  Yours looks to be uncirculated rather than proof.

N#21333

N#21336

N#15203

But no premium because of unormal heavy?

I don't know. I have never seen a modern US coin weighing 5% above the target weight so nothing to compare it to.  The mintage of this coin is so low that it would surprise me one was released well above the limit.  Check your scale. If it's accurate then have it certified as an error coin and see what people are willing to pay for it.  I don't think there's much of a market for over/under weight coins that are not wrong planchet types.