Setup: 3 clustered, database availability group Exchange 2013 servers running on Windows Server 2012 R2 (fully up to date)

Problem:

Our mail queue starts stacking up with error: 4.3.1 Insufficient system resources

I pulled out the transport log and found that once this error started happening a user was attempting to send a large file (400mb +) via Outlook 2013 as an attachment. Our send connector is configured to allow a generous 35mb maximum to message size. Why are my servers going into back pressure when technically the users message should be rejected immediately for breaking the send connector size rule? Or does Exchange have to process the file before rejecting it which is eating up my memory or disk space?

This has happened twice now due to users trying to send large files by Outlook 2013. Any suggestions?

Thanks!

Check your global message size limits.

Set-TransportConfig -MaxSendSize -MaxReceiveSize

https://technet.microsoft.com/en-us/library/bb124151

Thanks for pointing me in the right direction. 

Global message size limits were set to unlimited. I applied the standard using what you suggested and created a transport rule to analyze attachment sizes before they start bogging down my servers.