Candles frequently develop a larger flame as they burn longer. The heat of the wax as it melts and pools, the variety of wax, the variety of wick, etc. are all factors that come into play. Beyond this, there are much more subtle factors involved in the motion and action of something so simple as a candle flame than the easily noticed currents that we can readily perceive. For example, as the candle wax heats and pools it creates its own updrafts that impact the candle flame.
Telekinesis is a myth, and frequently perpetrated by con artists and stage magicians.