The phrase "at the end of the age" refers to the end of the Old Covenant age, not the end of the physical world. Jesus was speaking to a first-century Jewish audience living at the very end of that age. According to Matthew 24:3, the disciples directly asked Him about the end of the age, and He described the coming destruction of the temple and Jerusalem.

The burning of the weeds represents judgment on the wicked, specifically apostate Israel, which was fulfilled in AD 70 when Jerusalem was destroyed by the Romans. That event marked the final removal of the Old Covenant system and the full establishment of the New Covenant kingdom.

This fits perfectly with:

Matthew 24:34 – "This generation will not pass away until all these things take place."

Hebrews 9:26 – "...He has been manifested to put away sin by the sacrifice of Himself... at the consummation of the ages."

1 Corinthians 10:11 – "...upon whom the ends of the ages have come."

So the burning of the weeds at "the end of the age" is not a future event. It happened in that generation, just as Jesus said.