Check marks will appear next to each message you send. Here is what each one indicates:
In a group chat, the second check mark will appear when all participants in the group have received your message. The two blue check marks will appear when all participants in the group have read your message.
For any message that you send, you will be able to see a Message Info screen, displaying the details of when your message was delivered, read or played by the recipient.
To see the Message Info screen:
The Message Info screen shows:
Note: When a participant leaves a group, the Message Info screen will still show the original information with all participants, including the participant who left the group.
Learn more about the Message Info screen on: Android | Windows Phone.
If you don't see two blue check marks next to your sent message, these could be the reasons:
To turn off your read receipts, go to Settings > Account > Privacy and disable Read Receipts.
Note: This won't disable the read receipts for group chats or play receipts for voice messages. There's no way to turn these settings off.