Tight throttle spring on briggs ok?

David, This is what I found in google search for B&S carb. linkage diagram, you can also do a search because there are lots more.
Check the attached links,instruction and guides, Good luck
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Linkage Spring replacement on Briggs Stratton Quattro 4 HP Murray Lawn...
Repairing Lawnmowers For Profit Part 61 Governor Spring Help
briggs and stratton governor linkage diagrams Google Search
briggs and stratton carburetor linkage diagrams Google Search

John the governor is probably sticking, check for dirt and debris, make sure spring/ linkages are still attached, after cleaning lubricate linkages with lubricant WD or similar. Check the attached links,instruction and guides, Good luck
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Throttle stuck wide open Governor issues
Understanding and Adjusting your Governor on small engine
How To Adjust Mechanical Governor On Small Engines
Briggs and Stratton 8HP Throttle and Governor Setup

1. Move throttle control to wide open throttle position,
Fig. 45.
2. Loosen lever adjusting screw. Item 8
3. Turn governor crank counterclockwise and hold.
4. Torque lever adjusting screw to 15 in. lbs. (2 Nm.).

throttle spring could be broken stretched or missing

there should be a little screw to help adjust your idle try that..counterclockwise to add more idle, clockwise to slow idle..

Normally when you move the throttle control on the handle, all that is happening is that governor spring tension is increasing or decreasing pull on the linkage /governor arm. With engine off and plug wire removed, look for a small shaft coming out of the engine with an arm attached. Attached to the small arm will be linkage to the throttle on carb.. So when you move the throttle on the carb with your finger the arm moves also. There should be spring connected to opposite side of governor arm connected to throttle control at the handle or small lever or metal tab. When you incease pull on the spring, the engine will speed-up. Adjust as needed. Good luck

After researching the engine application, I see that this 675 is NOT an OHV engine. It appears it is the L (flathead) engine with the standard features. The 775-875 Platinum series mowers have OHV engine applications. That being said, many mowers have the carburetors with the governed throttles set to run at the the OEM mandated maximum speed. Some (like the Briggs Quantum series engines) have the throttle plate still attatched. You would need to bend it back up and install an aftermarket throttle cable assembley (like Murray makes). You would connect the carburetor end of the throttle cable to the hole in the plate assembly that has the governor spring attatched. Some even remove the governor entirely (internal governor has to stay in) and connect a throttle cable on the plate controlling the butterfly in the carb. Your unit may have this feature with the plate having a few different holes in it in which you could install the end of an add on throttle cable.

It could be that the governor spring has become disconnected or has broken on an end where it hooks onto the throttle linkage. If the spring is OK & throttle linkage is not binding it could mean the governor drive inside the engine has failed preventing the governor from operating correctly. You may need to take the engine to a mechanic to fix the problem.

One possible cause for this problem is debris,sticking,or frozen linkage between the governor and the throttle butterfly. Depending on the make and model of your engine it will either be a mechanical governor that has a arm that goes down into the case or a air vane governor that is behind the recoil shroud of the engine. Move all the linkage that connects between the governor and throttle and speed lever to make sure it doesn't bind or sticks. If it does pray a little silicone or wd 40 spray on it to help reduce friction. Also on air vane governors they can become stuck from debris that inhibits it from moving make sure there is nothing in the way of the governor. If all of the linkage is working properly and you still have the issue try adjusting the the fuel mix screws and the high rev. settings on the throttle lever (if equip.).

The engine speed is controlled by a governor and throttle position. There is a spring that holds the throttle (butterfly valve) against the slower position. When the motor is under load' the governor exerts force to open the throttle position. Make sure that all of the components are clean and not binding. Look for a broken or disconnected spring. It is also possible that the governor is stuck in the demand full throttle position.