Race Comment Explainer

Original comment with matches highlighted:

led until pushed along and headed 3f out, quickly,

Matched phrases & meanings

Phrase	Meaning
Pushed along	The jockey started to urge the horse (hand-riding, not necessarily using the whip).
tailed off	A definitive statement that the horse was finished and effectively out of the race
Weakened	The horse lost speed and dropped back through the field.

Summary

The jockey started to urge the horse (hand-riding, not necessarily using the whip).
A definitive statement that the horse was finished and effectively out of the race
The horse lost speed and dropped back through the field.