There are two main reasons why the police officer decided to shoot the elephant in "Shooting an Elephant" by George Orwell. However, weakness is not one of these.
The first reason for the police officer to shoot the elephant was because of his sense of duty. He knows that this is the job he is expected to perform, and although he is upset about it, he wants to fulfill his duty.
The second reason is that the police officer was worried about showing compassion in front of the Burmese. He argues that the British empire must appear strong and decisive in front of the people they have colonized. Therefore, he does not want the locals to see any hesitation on his part.