I don't know how many answers they will accept, as most are plausible, however, what I put, which is correct is that the higher current in the wire will heat it, due to it have finite resistance. The heat will increase resistance, in turn causing a drop in current.
Malfunctioning resistor is unlikely if the same resistor was used for all other values and all of them formed a straight line.
I'd imagine they may accept it if you said that one wire sample was bent until it work hardened, where resistance increases.
Voltmeters have very high internal resistance, so only a small current (microamps) flows through the voltmeter, leaving the overall current of the circuit largely unchanged, as most will still travel through the component that the meter is in parallel with.