texture weight

[pointythundra654]

I'm hoping I'm in the right channel so I've been doing textures for a while but it's only been read textures and I just recently got into meshes and I'm having trouble figuring out how to add weight to the texture so that I get wind movement the correct way in fallout 4 so I've added weight to my mesh but in game I I've got it moving but it also looks like it's breathing so it gets larger and smaller larger and smaller and I've been told that's because I need to add weight to the texture and I've yet to find some guide or tutorial that really explains to me how to do that because I'm not very good at understanding technical appreciate any help I can get

 

 

 

Edited March 9 by pointythundra654
Showing pictures to help show what my problem is