Too lazy to search for any good manga pages. So have sum wikipasta, because it explains his character pretty damn well:
"His drive for fighting is Jolyne. Selfless and valiant, he isn't afraid to risk his life for her. When they aren't in danger, he will use anything in his arsenal to woo Jolyne to his willies -though he is hardly successful and are moments of comic relief. Once he realizes that she is danger, he will jump into the fray with little regard for his own safety. In love with her courageous and burning determination, Anasui mused that given the chance, he would follow Jolyne for eternity.
Although he is devoted to Jolyne, he will treat anyone who isn't her badly. His noble and protective persona thins to show his otherwise menacing and intimidating tendencies. Whether friend or foe, Anasui won't hesitate to kill anyone who disturbs his happiness with Jolyne. On one occasion, he threatens F.F. to not interfere with his work, almost strangling her when she almost disobeyed. While he is more than willing to jump into action for Jolyne, he refuses to help anyone else unless he knows that Jolyne needs them. The main exception to this is of course, Jotaro, wanting his approval for his marriage proposal to Jolyne."