There are a few options in the Optimisation palette which can help you to reduce the file size.
As thematrix mentioned, you can reduce the number of colours. Also increasing the "web snap" will reduce the number of colours used and hence the
file size. The "lossy' slider increases the amount of unnecessary data that will be discarded, decreasing the file size even more. Play around with
these settings, but make sure you watch the preview, because they will effect the image quality when used too much.
Before you get to the optimisation stage you should first try to reduce the number of layers as much as you can. If any layers can be merged without
messing up the animation, then merge them.
Also try to ensure that the individual elements within the file are as simple and clean as possible. Bleeding, graded edges, colours and effects will
increase the file size drastically. For example in the below text, the amount of info in the second word is much larger than in the first because of
the motion trail effect using many more colours. If you can simplify elements without sacrificing too much artistic flavour, then this will help to
reduce file size.