Hi. Breasts morphing is handled through bones for the most part, so when they expand or shrink, everything in that area does as well. Putting anything between breasts ( or legs) in not a good idea.
You can try fixing it the following way but i cannot promise good results:
- click the + button next to rig, click those buttons until you'll see breast bones. When you will make them visible, you'll see them appear in 3d view. Select one, in pose mode press S 1.5 to make it bigger, do the same with the other;
- in modifiers tab enable those buttons on the armature modifier;
- disable Limit selection to visible and select the pull tab, deselect the area on the back and the breasts that will be selected as well;
- find breast bones in the vertex groups list and Remove their influence from the selected area;
- Normalize weights with Lock active disabled;
- inverse the selection;
- enable sync in uv editor and, holding Shift-Ctrl, deselect the torso;
- select one breast vertex group and lock the other;
- In weight paint mode enable Face selection masking for painting, choose Subtract brush first and try to remove a bit of paint to make a transition smoother. Choose Blur brush and try to smooth it further. Then lock this vertex group, unlock the other one, and do the same for it;
- after you're done, select the rig, in pose mode select all bones with A, Pose- Clear transforms- All