The posts do seem under-sized. I assume you bolted the frame to the posts. I would think about adding two more posts and diagonal framing at the corners.

They are 4x6 posts

They should have been 6x6 posts.

And the two beams should be doubled up. They are carrying a lot of weight.

Here's a link to a typical 16x16 pergola.

Pergola plans

(Unless you're using more than 2x8s. If that's the case, then maybe your structure up above is fine, but it's even more weight and that means your posts are definitely undersized)

When it moves, can you see the 4x6 posts deflecting from the ground up to the brace? I can see the nailed connection at the top of the posts loosening over time. Maybe some structural screws there would help.

Definitely 6" x 6" posts at a minimum, especially as this beams look like 2" x 12"'s. How thick is that slab and are those posts only anchored to the slab? Posts need a real footing.

Have no construction expertise but just by looking at it, the posts seem out of proportion with the top and quite puny and undersized.

Posts are too small and you need more of them . How are they put into the ground they need to be pressure treated and in concrete so is that what you have. IMO right now I would not wnat to be siting in there at all. That slab will be cracked in no time . There must be 100 You Tubes no how to build a pergola go there see what you did wrong and fix it before you kill someone or get someone to fix for you.

"and in concrete so is that what you have"

You do not want them in or in direct contact with the concrete. The appear to potentially be anchored correctly with a Simpson Post Base but do not appear to have proper footings.

Ok to answer everyone. No they are not 6x6. The slab is 5”thick and anchored to the slab. @seabornman no they don’t deflect from the bottom to the top. I used only structural bolts and screws. I’ve been debating on one side to build a bar that will strengthen the base not only does it add bracing but it’s functional

Why don't you add another 4x6 beside each post and through-bolt them together?

You need more support for the weight. Adding a bar won't give it more support. Unless you are also adding another post in concert with the bar. But that would only be support on that one side.

@greg_2015 I did think of adding and bolting through. what I’m having is not a weight issue. The weight is fine for the posts it’s more of a sheer issue. It can’t be pushed on the six inch side but on the 4 inch side is where we get the wobble Or shake or whatever. That’s why i thought of a bar on the side by the wall.

A 4x6 can hold up a whole lot more than what this relatively lightweight pergola weighs. Likewise the 5" slab. Maybe box out each post all 4 sides with 1x or 2x material to stiffen.

I'm not saying that the whole thing is going to collapse. But that weight is causing the posts to bend and wobble which is why you are seeing it wobble on the 4" direction and not the 6".

Another 4x6 might be overkill, but I think it would be the visually appealing alternative. It would keep everything symmetrical.

Even if this pergola didn't wobble at all, those skinny posts don't look right IMO.

@greg_2015 yes i would like them bigger and I’m not against adding another post. I just want to make sure this thing is solid so it’s not a danger. I was thinking of putting these on and seeing if it would help and then installing a bar in the space by the wall. the bar is both functional and bracing on that side.

Why didn't you use 6x6 posts to start with?

Okay, I'm confused. If you would also like them bigger, then why are you looking at alternatives that involve not making the posts bigger?

Add the sandwiched 4x6 posts and you have more than enough support and it's visually appealing. No need to also buy those additional brackets. Build the bar if you'd like, but again it isn't required if you add the additional posts.

Are the beams bolted to the posts? I see bolts on the diagonal braces, but I don't see anything between the beams and the post. Are they just screwed on?

@Brown Dog because they were more expensive and not readily available. That’s the only reason.

@greg_2015 they are bolted to the post yes. I’m looking at all options that will work. my first idea was to add another 4x6 making it an 8x6 essentially. I’ve just had a few people question if that would work. I assume I’d have to anchor the added post to the concrete yes?

@greg_2015 that would be way easier. All I would need to remove is a brace and re install that