Pump up, Jeez, boring grammar school weed (3,4)

I believe the answer is:

gym shoe

I'm a little stuck... Click here to teach me more about this clue!

This clue might be a double definition.

'pump up' is the first definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Maybe there's a link between them I don't understand?

'jeez boring grammar school weed' is the second definition.
I can't judge whether this definition defines the answer.

Can you help me to learn more?

(Another definition for gym shoe that I've seen is " It has gripping 'soul', you might say".)

I've seen this clue in The Sunday Times and The Times.

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