Getting back to the original question, the following points are relevant -
(a) for a constant power setting at constant level, a heavier aircraft will fly slower than the lighter example
(b) in a balanced turn, the load factor increases in relation to angle of bank
(c) one can view increased load factor as being much the same as increased weight (mass, whatever)
(d) ergo, turn and you slow down
.. for most of us, this is the typical calculation basis for a first approximation effect of turn on performance.
The underlying cause, as stated elsewhere, above, is that we need a tad more lift .. needs a bit more pitch ... which results in a bit more drag ... equals slow down. For the instructor who posed the question, the preferred answer should lie with the increase in load factor.