I think we ALL have tried to find ways to justify actions that our conscience doesn't allow us to feel 100% comfortable about. It's human nature, we do it to protect our egos. And it could be about a variety of issues. I know I've been there. Many of us have. The important thing is to realize where we're headed and try to fix the problem.
Bubli, assuming this story is true......most of the posters here give sincere/honest advice. And so far, very few (if any at all) are supporting your ideas. I think the majority of the people here have advised that you maintain a distance from your cousin. So, that says something.
You may be prettier than her. You may be more modern than her. But this isn't about looks or personality. You used a pinky finger analogy to describe the lack of closeness between your cousin and his wife. Well.........how do you expect her to get close to him if he's always busy with you? If he's always occupied in conversations with you....that leaves few opportunities for her to bond with him. That's not right, nor is it fair. Put yourself in her situation? This isn't even about her hijab or her being ultra conservative. Even "liberal" gori women would be upset if their husbands were busy with another woman and it wouldn't matter one bit if she was like a "best friend."
Do the right thing, hon. Maintain a distance from him. What you consider a light matter could be wrecking someone else's home. And you don't want that on your conscience. So take a break from him. Tell him to focus on his marriage and to make the effort to connect with his wife. Explain your reasons for wanting to maintain a distance. And if he's a MATURE guy who has even a drop of consideration for his wife and importance for his marriage.......he'll understand the effects of his actions because he'll put himself in his wife's shoes and try to understand how it makes her feel. No guy would like it if his wife was spending more time with another guy. We've given you the same advice. It may not be what you want to hear. But the final decision is up to you. I will say that had you felt 100% comfortable about what you're doing.....you wouldn't have felt the need to create a thread about it.