Got it! Where can I look for this fundamental concept? (i.e. how str(number) is ordered?, i.e. why '10003' <'22') Thanks!

Some info can be found in Python reference, but generally it boils down to paragraph starting with:

Sequences compare lexicographically using comparison of corresponding elements.
[... the explanation what "lexicographical comparison" is]

As strings, '2000' comes before '11'

How is it? '2000' is lexicographically greater than '11', isn't it? When compared as strings, 11 should come before 2000.

As strings, '2000' comes before '11' and both have a weight of 2 in input "2000 10003 1234000 44444444 9999 11 11 22 123" but in answer they want '11' before '2000' and then '10003' before '22', and these logic contradicts each other!

Could you explain how is the output correct?

Got it! Where can I look for this fundamental concept? (i.e. how str(number) is ordered?, i.e. why '10003' <'22') Thanks!

As strings, '10003' comes before '22' and both have a weight of 4.