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  1. He's well off. He can spend £ 1000 by (to?) the minute

  2. You can buy cheese by (to?) the kilogramme.

Do these sound correct? Meaning every minute / kilogramme.

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If you really mean:

He can spend £1000 every minute

i.e. £2000 in 2 minutes & £3000 in 3 minutes
then you want either of:

He can spend £1000 per minute
He can spend £1000 a minute

Neither "by the minute" nor "to the minute" make sense in this context, but might be used in other contexts.

I'm unclear about your second question: I don't see how it can mean "every kilogram".
I assume that you mean you buy cheese by weight and that the unit of weight used is the kilogram, in which case the correct form would be:

You can buy cheese by the kilogram.

The usage of "to the kilogram" does not make sense in this context, but could may sense in an example such as:

On average, you get 5 bananas to the kilogram.

That means that, if you buy a kilogram of bananas, on average you would get 5 bananas.

As regards spelling, note that the Oxford Dictionaries (ODO) state:

Kilogram can also be spelled kilogramme; both are correct, although kilogram is far more common.

Since you are using "£" in your question, I assume you are writing from (or referring to) the UK. The normal spelling used within the UK is kilogram.

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In the second example, the word by means as measured in. The problem with the first one is that the phrase by the can sometimes mean every - "He got sicker by the minute." Preposition use is very idiomatic with numerous patterns and exceptions. – bib Aug 3 '13 at 15:26

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