C3 is to increase the RF path gain but too much screws up the modulation signal high freq rolloff corner. The RF will draw up the bias on C3 during positive RF cycle (like an emitter follower) but there is only the resistor to pull it back down during RF negative cycle.
With a 10k collector load resistor the modulator will not work at a very high RF frequency, maybe 200 KHz. Loading capacitance will reduce high frequency gain.
You can see the effect in a simulation as a distortion on the AM envelope.