Question

Two identical solid pieces one of gold and other of silver when immersed completely and water exhibit equal weights when weight in air given that the density of gold is greater than that of silver who will be more

Answer 1

When the two materials are in the water , the less thick / dense material  i.e. Ag possesses a more prominent volume than the more dense Au. So it has more upthrust from the water and, in spite of the fact that they both demonstrate a similar weight submerged, there will be more mass of Ag present. Thus, out of the water then the Ag would weigh more than Au.  

When by weight you implied the power of gravity upon the material, at that point by the definition, the two materials had a similar force of gravity so they would have a similar mass.

F = w = mg