Nice question. What I think is virat's nature has two main qualities...
1. Him not speaking enough
Living in joint family, he inherently knows when to shut up. He was raised under authority. There is no 'freedom' to make his choices. When you know you cant do much, then automatically you tune your actions and expectations. He was just behaving like this till Sai entered his life.
When he met Pakhi, still he was thinking from his family point of view tht Pakhi might be the right dil. He was taking decisions 'for' his family than himself. Sai is the first decision he took as an individual without anybody's influence. He always had the ability to make choices for himself and he did. He continues the same with Sai and his life. Be it her education, standing up for her and making her dreams his priority he makes these choices for him and Sai together, not for the family. That shows he is learning to make his 'own' small family...still confirming to the larger joint family he lives with. In his family, he has full freedom and exerts authority. But when he tries to fit 'his' family with larger family, friction happens because he has to roughen the edges a bit. For me, it is organic that he behaves this way. He has something of his own, his dependents for whom he has to stand up for. He is still trying to balance these two: personal space and joint family space that he sometimes doesnt know how to respond. Hence, we feel he has to do much more when it comes to Sai and we forget that he is still 'figuring' it out.
2. His tendency to show sympathy towards Pakhi.
I am still not sure if my thinking is correct but from What I analyze, may be from childhood he saw his mother suffer without support. He has so much respect for his mother because of how she raised him despite the treatement meted out to her. His peace making attitude definitely comes from her. He knows what 'real' suffering is from his mother so he doesnt pitch in much for smaller issues in the house and stays silent. But seeing her mother, he must have developed sympathetic attitude towards women who are suffering or without support. This I could say from KD's story again. Here we dont know this quality of his yet. But if you see KD story, he goes to extreme extents to stand by the women who dont have support. Be it shruthi or Pakhi in the end. He gets pulled towards them, keeping his wife at stake. This is a tendency I guess. It is not romantic absolutely. Just the need to stand and support a suffering woman. But again this is just my guess.
3. Insecurity and jealousy
The above two are his main characteristics according to me. I think insecurity and jealousy are just because of Sai and the circumestances in which they are married. And ofcourse the age gap. Till they become one emotionally and physically, these things are bound to happen. There is no security of love or intimacy to clear their doubts. These feelings are new to them so he behaves in extreme manner. Added to it, there is an inherent male ego that comes into play when Sai goes against him in these matters. Be it PD lunch, or eloping Devi and now moving close to classmate. Do you think if they had expressed their love and had conjugal relationship, these things will cause an issue? I guess No. they would have discussed it casually in the confines of their room and probably Sai would have playfully made him jealous about her classmate and shared a laugh together.
So 3rd part is a passing phase for him, but not for Sai. She has deep rooted insecurity for him unlike Virat's and Pakhis presence has already made it so strong that it takes time for her to come out of it. She repeatedly suspects him of infidelity (His mistake too to prioritize other women). That discussion is for another day.!