The thoughts of the old man as he dances with Leila are actually very well mapped out for the reader through what he says to her. He is clearly reminiscing about his youth and how quickly old age comes. He talks about how he has been dancing for thirty years and therefore he is definitely thinking how quickly somebody like Leila will fade and become old, even though she appears to beautiful and young and it is her first ball on this evening. Note what he says to her about what will happen to her before she knows it:
And you'll smile away like the poor old dears up there, and point to your daughter, and tell the elderly lady next to you how some dreadful man tried to kiss her at the club ball. And your heart will ache, ache...
Presumably therefore the fat man is thinking of how his own heart is aching with the passing of time and the ephemeral nature of youth and beauty. His words have the impact of temporarily denting Leila's keen pleasure and enjoyment of her first ball, though not for long, as she quickly forgets the old man as she relishes her youth and beauty while she has it.