The question is one of financial infidelity.
Your wife will never accept it, fully. But, if she believes that you are totally into it she will give you some breathing room. Once you have quite a few watches she wont actually know what is going on or care how many watches you have.
Dont try and get her into the hobby, wont work. Also, dont ask her how she feels abot your newwatch, she will let you know exactly by how she looks at you.
My advice, tell her you want to have a collection / hobby and justify it by saying I am going to spend £??? a month, every month. All hobbies cost money and you only get one life. If you are delivering on everything else fight your corner, thats how she wil know you are serious. After all, how much does her hair or nails cost? etc. Then buy some affordable pieces and start flipping.
After 10 years of this, a package arrives and she gives me a look but says nothing. Cool.