What causes a 17hp briggs to surge on high speed and run rough at mid and low speeds?

Likely dirty jets in the carb that need cleaned. Varnish and gum buildup are leaning the mixture out resulting in the surging.

Thanks Smoothy I have already cleaned carb I thought that was the problem also. It idles rough and at mid throttle it is rough,then you get above that it starts to smooth out then after it warms up is when the surging starts to happen. Could there be a crack in the manifold or a warp in one of the mounting surfaces causing this? (say a vacumm leak? )

I'm a bit leary about saying vacuum leak because those are typically far worse at the lower speeds because the volume leaking is a greater percentage of the intake volume at the lower speeds. The leak would tend to be constant.

Did this happen all of a sudden? Or was it gradual that it got this way?

At this point I'm thinking Ignition. Perhaps the woodruf key on the flywheel has sheared and its moved off time? Have you done a compression test or checked the valves recently as two other things to check.

I think I have a service manual for this series engine at home I could look at tonight and see if it says anyhthing. I've never really dealt with something like this that wasn't carb related before.

Yes it did but the mower belongs to a friend who has a small lawn service he said he killed the mower in a drive way, when I say killed he had the deck on and snuffed it out completely. Saying that I did adjust the valves,checked the key way and cleaned coil and flywheel then give it back to him to use. It lasted about 30 minutes then a puff of blue smoke came out. I checked the valves again,thinking I messed up but didn't,checked key way again,cleaned carb and still can't figure it out. It does have good compression also. This has got me frazzled.

Yes it did but the mower belongs to a friend who has a small lawn service he said he killed the mower in a drive way, when I say killed he had the deck on and snuffed it out completely. saying that I did adjust the valves,checked the key way and cleaned coil and flywheel then give it back to him to use. It lasted about 30 minutes then a puff of blue smoke came out. I checked the valves again,thinking I messed up but didnt,checked key way agian,cleaned carb and still can't figure it out. It does have good compression also. This has got me frazzled.

Sort of has me stumped too... but we have other people that do this for a living and not a hobby that will answer in due time. Hopefully they have some better ideas to add.

You are sure its not dropping a cylinder at intermittant periods that's looking like a surge as it starts and stops firing? I've had plugs fail like that on one of these, not once but twice in the last 3 years.

Check your fuel cap make sure its venting .
Try it with and without the air filter on.
Check your block vent coming to carb.

I did try it with the air filter off, no difference, block vent is black tube coming from breather correct? I checked it, no blockage. The surging happens after it has been run for about 20-30 minutes

I've gotten discusted with this thing,between asking everybody what's wrong with this thing and doing all suggestion and nothing working. Now this thing has started backfiring again like the valves are out at start up. Still got same surging problem as before,don't know where to go next anybody got any suggestions?