I was watching recent activity on this old thread, so to resurrect it and address the problem {finally

} the answer is simple:
The kart never had brake return springs. The natural springiness of the brake band(s) acts as its own return spring. Your kart has two brakes, one on each side, and a transverse rod across the kart frame which acts as a lever (and a force multiplier) and permits one pedal to activate the two brakes.
Maybe the brake band is making contact or "riding on" the brake drum too much for the OP's liking? Some contact is natural but I would make certain the entire brake system moves freely and easily and that the brake band 'bounces back' off the drum instead of binding. This might take some real effort with penetrating fluid (Liquid Wrench, PB Blaster etc) AND removing all the corrosion, pitting and roughness that rust causes, from the entire brake linkage system.
For the transverse rod, I think it is welded to the frame, so to free it up and ensure that it moves with absolutely as little resistance and possible, I would disconnect the brake linkages from it and work it manually with your hand and bathe it in penetrating fluid

around and around,

back and forth until it is free.
For any part that has a bore or hole, like the loops on both ends of the brake band and the brake pedal pivot hole, use a round brush like a .22 to .30 caliber rifle bronze/wire cleaning brush. Chuck the rifle brush of the appropriate size into an electric drill and spin it inside the loops or holes until they are smooth. Then lubricate everything with a medium oil like motor oil, 3-in-1 oil or grease. Do not use WD-40 as it is too light, it is basically a solvent and does not last.
Everything with a red arrow (or any part that moves the brakes) and parts #66 and #67 needs to be as friction-free and smooth as possible:
I don't know anything about this cart besides its a carter brand so if anyone know anything about this model let me know!
It appears to be a Carter Brothers 1735 Hot Bodies® or a 1755 Super Wheels®.... these frames are basically identical but probably involved a color change, name change, sticker change and voila! They have a different kart.
Store your karts INDOORS, folks.



