I think
The Bat! can do it.
I know that you can do
1) "receive header only if message is greater than X kb" (under Account: Properties: Mail management: Message management)
2) "show me what's on the server (new or all messages) and the first X lines" at which point you can see the message size and attachment name and choose to download or delete from the server (Account: Properties: Mail management: Mail Dispatcher)
If you want to just delete them outright, I think you can setup some heavy duty filtering such as "if the message has an attachment and is greater than X size, delete it from the server" (Specifically, go to Account: Sorting/Office filters: Incoming Mail: New, then for Action = "delete mail from server" and Advanced = "message has attachments" and "message is larger than X kb" and I think that will do it.)