How would you interpret this phrase ‘weigh in my favor’?
Naturally, you may have a different opinion. Let me sum up a few details and be finished, so you can consider the offer. Weighing in my favor, I hope: I am likely in a position to exceed your present salary. A drawback: my workplace is here where I live. Some ladies might find it awkward to work in the home of an unmarried gentleman.

How would you interpret this phrase ‘weigh in my favor’?
Thanks!
PS: It’s a part of a letter in which a gentleman wanted a lady to be his secretary.

Question

How would you interpret this phrase ‘weigh in my favor’?
Naturally, you may have a different opinion. Let me sum up a few details and be finished, so you can consider the offer. Weighing in my favor, I hope: I am likely in a position to exceed your present salary. A drawback: my workplace is here where I live. Some ladies might find it awkward to work in the home of an unmarried gentleman.

How would you interpret this phrase ‘weigh in my favor’?
Thanks!
PS: It’s a part of a letter in which a gentleman wanted a lady to be his secretary.

Answer

"Weigh" here means "influence your decision".  "in my favour" means "to my advantage".

"Weighing in my favour" means "(A factor) influencing your decision so that you may choose me".

Answer

Ben's answer is correct.  Here's a bit of background to understand and remember the meaning of the phrase.  The "old school" way to weigh things was with a balance scale.  You would put a known weight on one side and the unknown weight on the other side.  If the known weight was lower than the unknown weight, that meant the unknown weight was less than the known weight and vice versa.

From this came the metaphor of "weighing" the value of something by putting the negatives on one side and the positives on the other.  So, for example, one could say "X weighs in your favor but Y weighs against you".