We have two large exterior exposed cypress beams/posts, that are part
of the structural wall and roof support of a breakfast nook area (back
patio area) that have developed rotted bottoms. I've been putting
off this repair because I'm not sure, exactly, what might be the
best/proper repair. Obviously, moisture has wicked up the posts for
some time, and the bottoms are rotten. Left and right side posts,
scroll left: https://www.flickr.com/photos/43836144@N04/16411478004/

I wouldn't waste my time with fillers or stabilizers. If you want it to
last, replace the posts.

I can't tell for sure from the pictures, but the one that has the propane
tank looks like the bottom of the post may have already been replaced at
some point. About a foot from the bottom the grain doesn't line up.

The exposed posts would be fairly easy to replace. Just use a bottle jack
and a shorter post to jack up the structure slightly. Don't go crazy
jacking it up, you just want to take the load off the existing post. Then
cut the old post out and install a new one. Ideally you should install a
metal post base at the bottom of the post to prevent water from wicking up.
Barring that, I would at least put some tar paper or sill sealer under the
post as a water barrier. Not ideal, but better than nothing if you're not
going to use a post base.

The ones that are inset into the structure are going to be a bit more work.
You may have to cut the structure away from the posts, then jack up and
replace. You will most likely need to repair wall surrounding the posts
afterwards. I don't know how it's all put together but it may be easier
just to take the wall down and rebuild it after replacing the posts.

Good luck,

Anthony Watson
www.mountainsoftware.com
www.watsondiy.com