There are many online wallets like Xapo and Coinbase that do not charge any transaction fees or they pay that fees by themselves. I want to know that how would they profit from paying for their user's transaction fees ?
If no fees is charged then the transaction take a much long time or even might get cancelled !
As it's been said, there are sponsors, premium features or whatever (some sort of advanced service for certain people), and Xapo and Coinbase are an exchange as well as a wallet, so they make money off of people exchanging Bitcoin and USD on their site. Having a wallet there is just a plus, and something to keep people using them.
Plus transaction fees are typically pennies, so it doesn't really matter.