I agree with Roger, to check out your posts in concrete.
It's been my understanding that if you put a post into a hole and then fill it with concrete to hold the post, you are creating a cup with the post in the middle. If the bottom of this giant concrete cup has a hole in it for the water, (whatever water may get into it, from anywhere) to run out then you might be ok. But if the concrete cut doesn't have a hole in it, then the post is sitting in water. Water rots wood. There is (I've been told) no such thing as dry rot. Water, if it gets in this cup, will rot your posts.
Now if this building has been standing for years and there is not apparent damage you maybe ok. But who knows. You could have a problem you don't know about and adding weight to the structure could cause problems.
Good luck with your project,
Jim