She is not there yet! There are miles to go for Viaan to make Katha fall in love with him but for now he knows his feelings and is contented that he has fallen in love!!
Love is an emotion that he has just understood and experienced. What it feels like to just have one person in your life that gives you hope. He sees that hope in her and wants to hold on to it.
Love is journey and he is ready to take on that journey and experience the highs and lows along. His mother tells him that loving her will not be easy. He never thought it would be easy either, but he is willing to take his chances as he sees no way around. It is his journey of love, his trials and tribulations. He sees her still entangled in her past but with his love he hopes to find her somewhere in this journey of life.
Katha is living in her dead husband's memories and is not there yet to allow herself to love anymore. She made it clear to him but what she does not know that his love can wait endlessly with a hope that she will come to him one day. He wants her to give love another chance, and he does not mind waiting for her from a distance and not come in her way. Love makes you patient and also kind and Viaan is just experiencing whole gamut of emotions and becoming a better person from it.
Down an unknown road to embrace my fate
Though that road may wander, it will lead me to you
And a thousand years would be worth the wait
It may take a lifetime, but somehow I'll see it through
(lines from Go the distance, Hercules)