Help with Briggs carb

I'm looking for service and tuning info for the common Briggs flathead carb that mounts on top of the tank. The motor is the common 3.5HP horizontal shaft version typically used on mini bikes and is in great shape and completely stock with the standard muffler and air filter. Carb has been cleaned and has fresh parts installed. I didn't do the work so I am not familiar with the inner working of the carb.
The engine starts and idles but has a lean stumble if more than 1/4 throttle is used during acceleration. Once the bike gets up to around 20mph you can crank full throttle and it runs good and pulls strong.
The horizontal carb appears to have only one removable brass jet that I am guessing is the idle jet. I don't see any mixture adjusting screws on the outside.
Any help with written material or suggestions will be appreciated.
Steve O'Hara
Steve, That removable jet is booth the idle jet and main jet. With the jet out, look in the hole and you will see a small front hole and a larger rear hole. The closed butterfly blade is on the inside of the front hole.You could enlarge the front hole a tad, but open the butterfly as not to hit it with a drill or reamer. That probably isn't needed as the jet should have a adjustable needle that screws into it? 1 1/2 turns out should be a starting point. Sometimes the fiber washer behind the needle adjuster is flattened from age and use and a double washer will help the space between the needle and jet. Much more than 2 turns out on the needle could be telling you to enlarge the brass jet hole a tad.
And I'll add, you will have to be a little fat off the bottom to get it to transition from low to mid, these carbs don't really meter the whole range as well as we want them to, not near as well as a little slide carb would.

Thanks guys.
Here's a photo showing the location of the jet on the carb and the jet itself when removed.
On this carb the jet screws in and seats in a fixed position and there appears to be no adjustment options other than to the drill the jet. The controlling orifice down through the center of the jet is about .019".
Based on Freezeman's description I think he is talking about a different type of carb.
since this setup has no adjusting needle or fiber washer.
Another thing to mention... if I get this engine revved up past the flat spot and then let off sometimes it will backfire. That is odd because a backfire is usually from a rich mixture on the run down. I know very little about these old four bangers.... haven't run or worked on one since around 1967 so bear with me. If it was a two cycle pumper carb it would already be fixed LOL
I checked all the gaskets to make sure there aren't any leaks in the intake tract and all looks good.
Any other suggestions?
Thanks again.
Steve O'Hara
Ya Steve most of us on here are more familiar with the 5hp carb, which was what freeze was describing. At .019 , it's possible that all the metered fuel is passing thru that jet. The 5 hp runs a .036 jet. If so, increasing it's size will help the transition but may make it too rich on top, where these 4 cycles need to lean out. That's why I say it's hard to get that style carb to do everything well. Better get a spare jet if your gonna try drilling it, and take it up .001 at a time Jon
From his decription the start with I felt its the new style pulsa jet carb and you guys were thinking old style..
Indeed after the picture its was the other,, new style..

I feel you still have a tic of fuel restriction as assumed by them.. BUT the thing you need to look at first is the main fuel jet thats on the bottom of the carb thats sticking into the tank.. Its either directly on the bottom or on the side near the bottom of the down spout.. Which on this carb is cast material just like the carb,, The needle you have in your picture is not your culprit..

One other possibility,, on the side of carb ABOVE the tank theirs a welch plug,, behind it you will find the metering holes they spoke of,, the smallest could be partially stopped up.. DO NOT enlarge much more than they are already.. Small one is approx .026..

BTW the brass jet in the bottom I spoke of,, its non replaceable,, so again don't over enlarge..

Thanks for the feedback. These old carbs have changed since I was a kid. Back in 1966 when I got my first Taco mini bike it had a 3hp Briggs and it didn't take long to learn how to disable the governor. With the governor bypassed the engine would run lean at the factory settings but I recall there being an adjustable mixture screw that I could tune. No adjusting screws on this thing.
This carb has the welch plug on the right side of the carb and a big one on the rear.
About the pickup down in the tank... some questions.... With the motor running I removed the gas cap to see if it behaved like the cap was causing some restriction and I noticed that the thing pumps a lot of fuel.... there was a large steady stream of fuel dumping out the bottom of the carb back into the tank. Is that the way these things are supposed to work... like a pump around system built right in the tank??? Seems like there is a pickup that extends down into the tank that stops just short of the bottom and it looks like it pumps fuel up there and what it doesn't need just falls back into the tank???? It's funny, I always thought these old carbs worked on a siphon effect but this thing sure seems to be pumping a large volume of fuel around in there.
Without having taken the thing apart or seeing any diagrams I am still trying to get a general idea of the system before dismantling it.