Answer:
He stopped dead in his tracks on his way back from the bakery because he overheard people in strange clothing saying something about Harry Potter which sounded an awful lot like his nephew's name, and after a day of peculiar happenings even more evidence was pointing towards his worst fear.
He suddenly decided to give Harry Dudley's second bedroom because he was afraid the wizarding world would find out how neglectful and abusive they are towards Harry. With the swarms of letters he knew that Dumbledore and the wizarding world were onto them. It was not out of sympathy in any way, it was out of fear.