Can you post your Troubleshooting Information? At the top right of the Thunderbird window, click the menu button , then select Help, and then Troubleshooting Information. Press the Copy text to clipboard button and paste the information into your reply.

Application Basics

   Name: Thunderbird
   Version: 38.4.0
   User Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.10; rv:38.0) Gecko/20100101 Thunderbird/38.4.0
   Profile Folder: Show in Finder
   Application Build ID: 20151119061742
   Enabled Plugins: about:plugins
   Build Configuration: about:buildconfig
   Memory Use: about:memory

 Mail and News Accounts
   account1:
     INCOMING: account1, , (pop3) inbound.att.net:995, SSL, passwordCleartext
     OUTGOING: outbound.att.net:465, SSL, passwordCleartext, true

   account2:
     INCOMING: account2, , (none) Local Folders, plain, passwordCleartext

   account3:
     INCOMING: account3, , (imap) imap.googlemail.com:993, SSL, passwordCleartext
     OUTGOING: smtp.googlemail.com:465, SSL, passwordCleartext, true

 Crash Reports
   http://crash-stats.mozilla.com/report/index/bp-4031cd70-3d67-417e-ab14-5caca2151127 (11/27/15)
   http://crash-stats.mozilla.com/report/index/bp-e9690e54-71fd-49bb-900a-70f5f2151025 (10/25/15)

 Extensions
   Lightning, 4.0.4, true, {e2fda1a4-762b-4020-b5ad-a41df1933103}

 Important Modified Preferences

   Name: Value

     browser.cache.disk.capacity: 358400
     browser.cache.disk.smart_size_cached_value: 358400
     browser.cache.disk.smart_size.first_run: false
     browser.cache.disk.smart_size.use_old_max: false
     extensions.lastAppVersion: 38.4.0
     font.internaluseonly.changed: true
     font.size.variable.x-western: 18
     gfx.blacklist.direct2d: 3
     gfx.blacklist.layers.direct3d9: 3
     layers.acceleration.disabled: false
     mail.openMessageBehavior.version: 1
     mail.spotlight.firstRunDone: true
     mailnews.database.global.datastore.id: e79f43ed-d324-f841-b24f-46964715a02
     mailnews.database.global.views.conversation.columns: {"threadCol":{"visible":true,"ordinal":"1"},"flaggedCol":{"visible":true,"ordinal":"3"},"attachmentCol":{"visible":false…
     mailnews.database.global.views.global.columns: {"threadCol":{"visible":true,"ordinal":"1"},"flaggedCol":{"visible":true,"ordinal":"3"},"attachmentCol":{"visible":false…
     network.cookie.prefsMigrated: true
     network.predictor.cleaned-up: true
     places.database.lastMaintenance: 1447732688
     places.history.expiration.transient_current_max_pages: 104858
     plugin.importedState: true
     print.macosx.pagesetup-2: PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0iVVRGLTgiPz4KPCFET0NUWVBFIHBsaXN0IFBVQkxJQyAiLS8vQXBwbGUvL0RURCBQTElTVCAxLjAvL0VO…

 Graphics

     Vendor ID: 0x1002
     Device ID: 0x6740
     WebGL Renderer: false
     GPU Accelerated Windows: 2/2 OpenGL

     AzureCanvasBackend: quartz
     AzureSkiaAccelerated: 0
     AzureFallbackCanvasBackend: none
     AzureContentBackend: quartz

 JavaScript

 Incremental GC: 1

 Accessibility

   Activated: 0
   Prevent Accessibility: 0

 Library Versions

     Expected minimum version
     Version in use

     NSPR
     4.10.10
     4.10.10

     NSS
     3.19.2.1 Basic ECC
     3.19.2.1 Basic ECC

     NSS Util
     3.19.2.1
     3.19.2.1

     NSS SSL
     3.19.2.1 Basic ECC
     3.19.2.1 Basic ECC

     NSS S/MIME
     3.19.2.1 Basic ECC
     3.19.2.1 Basic ECC

Do you have any other issues on this computer accessing the Internet, or just Thunderbird?

Try to change 'Authentication type' in your Thunderbird Gmail account settings to 'OAuth2'. You'll be prompted for your Google password. You'll get another prompt to allow Thunderbird to access your Gmail.

I changed the Authentification type. It did save but did not ask though it did prompt me for Google password (or another prompt to allow Thunderbird to access my Gmail. This had no affect on sending email.

I have no other problems with the Mac other than Thunderbird. I do have another problem with Thunderbird in that when I set up new folders they do not appear in the folder list . Previously this worked fine.

Thanks for the help.

This had no affect on sending email.

You'd need to make the change to OAuth2 for the Outgoing Server (SMTP) as well.

when I set up new folders they do not appear in the folder list .

I'd suggest you start a new thread for this.

Although I thought my problem was solved (and I indicated it was solved) once I changed to OAuth2 for the Outgoing Server, it improved only for a few days and has now recurred, taking even longer to send messages.

Any other suggestions? Thanks

Try to start Thunderbird in safe mode. https://support.mozilla.org/en-US/kb/safe-mode-thunderbird

Is there any difference?

I did disabled the add-ons. A substantial help. Small files go through quickly. Larger files of 2.8 to 12 MB sizes take from 13 to 48 seconds to transmit - being 9 to 15 seconds longer than sending the same files using my AT&T/Yahoo account. Is this what I should expect?

And, I see oddities such as sending the same large 18.9MB file twice once taking 3:41 and then taking 1:15 (1 minute 15 seconds) to transmit), though this is certainly an outlier.

I did disabled the add-ons. A substantial help.

According to your Troubleshooting Information your only add-on is Lightning. Are there others?

I'd not expect that Lightning would have any impact on the time it takes to send messages with attachments.

Obviously the time it takes to send messages with large attachments directly depends on the speed of your Internet connection. Depending on what technology is used this can be variable.

Regardless of that, email is not necessarily the preferred way to transfer large files. Take a look at the Thunderbird Filelink feature. https://support.mozilla.org/en-US/kb/filelink-large-attachments

It works well for me in connection with Dropbox. https://addons.mozilla.org/en-US/thunderbird/addon/dropbox-for-filelink