Having tears in eyes is not a sign of weakness , hiding it certainly is.
It is very common for sensitive people to get tears on listening to roohani gaane.
At times it is for beauty of lyrics (jinhe naaz hind pe hai wo kaha hai, tujhse naraz nahi, do naina aur ek kahani, katra katra) or iallt is because of arrangement of music (satyam shivam sundaram, parvat ke is paar), it all depends on how you feel about the song.
And this song ye jo desh hai tera (swades) often brings tears because of lyrics & pic in film.