I'm quite sure it's Gan-Kon (English title: My Wife Is Beautiful God).
Tagamori Shinta is a student who routinely confesses with complete sincerity to any girls that he likes, failing every time with good reason. One day, after another failed attempt, he stumbles upon a strange shrine and ends up making the most important wish of his entire life. A romantic comedy packed with action on a celestial scale.
The main character battles with the red thread of fate, which becomes thicker the more affection he has towards the girl (his god).
After every winning battle, his god gets more territory and her shrine is also upgraded accordingly.