Analyze the formula w= mg to explain how an objects weight can change even when its mass remains constant.

Not sure about analysing, but the mass is how much matter an object is made of and weight is the downward force acting on the object. So, really, when we measure ourselves, we're measuring our mass, not our weight, because mass is measure in grams or kilograms, and weight is measure in Newtons.

Ohm's law tells you that i = v/r where v is equivalent voltage and r is equivalent resistance of the circuit
since all circuits have the same voltage, your question is really asking which circuit has the lowest total resistance, since the lower the resistance, the higher the current
circuit a has a resistance of 5 ohms; circuit c is in series so has a resistance of 10 ohms; circuit b is in parallel and therefore has a resistance of 2.5 ohms (review your notes on adding resistances in parallel and series); therefore b has the highest current