That is a good Question :
I will give the solution for the cases when the That concerns the weight Asssuming that the description of the trough to be approximately cylindricial shaped. These kind of questions are to be dealt under the assumption that the air doesnot escape from the top of the container after the melting of ice

NOw for the weight of the fluid after ice has melted

Now the combined weight of the ice and the air = upward B force= weight of volume of the liquid displaced
No lets us assume that the weight of air is m
Now when the ice melts the air goes over the liquid and exerts a downward force on the surface
nOw the entire air is exerting a downard force on the liquid
the downwards is equal to mg
Since the force exerts a pressure P at the surface of the liquid
All the elements of the liquid experience this pressure and therby the force exerted on the wieghing sacle also increases
Now the net Force on the wieghing scale
Weight of water +force exerted by air
The force exerted by air = weight of the air
Weight measured = (weight of water +Weight of the air)
Now I have explained the final scenoria
Now let us see the initial state
Now assuming that the balance is a weighing balance
Initiall the ice cube is floating on the surface of water so the there is B force of magnitude= (weight of water +Weight of the air)
Now the ice cube exerts A reaction force on the liquid
Now this measured reading of the weighing sacle is certainly greater than the final reading
Therefore the The reading falls
If it were to be a spring balance then the reading remain the same


NOte : In this kind of Questions (without air) all the books say the Initial weights = Final weight
But they don't mention that the measured weights are with respect to spring balance
So therefore in this problem too we consider the case of a spring balance rather weighing balance

Therfore the final ans is that the reading falls
Now the level of the liquid after the ice has melted

--Hope this helps