1 Unit of enzyme is defined as "an amount of protein that produces 1 µmole of product per minute". The thing that causes the problem is the word "amount".
The "amount" is not a mass, it is, for want of a better word, a 'blob'. You can buy enzymes in 'Units'. You buy a vial that will contain a number of Units of enzyme. You then know that if you dissolve the contents of the vial in a solution how many µmoles of product per minute will be produced. If you buy 1 Unit of a particular enzyme from two different suppliers you may have vials that contain different weights of powder, but the work that can be done (i.e. the amount of product produced) will be the same.
Look at these two 'piles' ('blobs') of enzyme:
Pile 1 of Enzyme
Pile 2 of Enzyme
Both 'piles' contain the same number of red balls (i.e. 4), and if 4 red balls are need to produce 1 µmole of product per minute (i.e. 1 Unit) then both piles can be said to contain 1 Unit of the enzyme, and yet, as you can see, there are many more balls in pile 2... Pile 1 is certainly more pure as there is less contaminant (yellow balls) around.
This is why 'amount' in "an amount of protein that produces 1 µmole of product per minute" is not a weight, it is, an 'amount', it is a 'pile', a 'blob'....
If you have problems with 'Sciences Maths' then you might like to check out some of the courses over at Maths4Biosciences.