Have you tried deleting the app's cache? Long press on the messages icon, tap the circled "i" in the top right corner and then scroll down to "storage". Once there, tap the "storage" text and down at the bottom select "clear cache". See if that speeds things up. You can also clear the data if the cache clear does not work - it will not delete your messages, worst that happens is you will have to log back into the app. Unlikely, though, since your phone is already logged into your Google account.
