I have several emails with large attachments that I want to forward to a particular email address. I can't forward these emails as attachments, because then the resulting email would be too large. How can I forward all the emails without having to send them manually one at a time?
Are both email accounts available on the same Thunderbird instance? If so, you can simply move the email to the appropriate folder on the other account. This works with incoming message filters.
If that is not possible, the standard way of doing it would be to apply a filter on the server rather than the client. Of course, that doesn't involve Thunderbird and would require some access to the server unless the server is running IMAP with Sieve filtering installed. Update your question if needed and I'll expand this part of the answer.
Basically, if you cannot forward the email, your options are very limited. There is, though, one other possibility. Thunderbird now allows you to use external storage for attachments. You can use Box.net, Ubuntu One and YouSendIt to store attachments and get Thunderbird to send just a link.