A Tale of Two Cities is largely about influences and interconnections. The echoes represent the consequences of characters’ choices and influences.
Consider the corner of the house where characters seem to sit and think. It is a corner for echoes, because the one sitting there can reflect on the events of the past, choices, and the potential of the future.
It is no coincidence that Dr. Manette's house is mentioned as the spot for the echo.
The corner has been mentioned as a wonderful corner for echoes; it had begun to echo so resoundingly to the tread of coming feet, that it seemed as though the very mention of that weary pacing to and fro had set it going. (Book 2, Ch 6, enotes etext p. 64)
Darnay, the character whose past always seems to catch up to him, comments about this.
I have sometimes sat alone here of an evening, listening, until I have made the echoes out to be the echoes of all the footsteps that are coming by-and-by into our lives. (Book 2, Ch 6, enotes etext p. 66)
Darnay is often a victim of others’ choices, but he made the choice to marry despite his past. He realizes that he can never truly be free of his past, and the echoes will catch up with him. When Carton responds that their lives will be crowded, he is foreshadowing the trauma and pain that is ahead of them with Darnay is targeted by the revolutionaries.
Consider Lucie’s thoughts on the echoes.
For there was something coming in the echoes, something light, afar off, and scarcely audible yet, that stirred her heart too much. (p. 136)
The events of their lives, including their daughter and the events when her doomed family returns to France, are foreshadowed.
The echoes get more insistent.
But, there were other echoes, from a distance, that rumbled menacingly in the corner all through this space of time. And it was now, about little Lucie’s sixth birthday, that they began to have an awful sound, as of a great storm in France with a dreadful sea rising. (p. 137)
This is the beginning of the end of the family. All of the choices of the past, including those of Dr. Manette, Charles, and Sydney, are about to catch up to them.