I'm having problems with my engine stalling on heavy acceleration and speeds over 40 mph when I have less that 10 gallons of gas in the tank.
If the gas tank is full the engine runs fine (except for a small hesitation at full throttle from a complete stop, no problem from rolling 30 mph acceleration )but if the tank has less that say around 10 gallons the engine starts to sputter and stalls if I go over 40 mph. I can limp along at 35 all day long. As soon as I fill the tank the problem immediately stops. I'm running a stock 350 (may have a what I was told was a LT1 cam)with a Rochester carb.My first thought would be the fuel pump but with a full tank its fine. Maybe collapsing fuel lines ? Thoughts?

 

Sounds like a weak fuel pump ready to fail. Without the additional head pressure of a full fuel tank it doesn't want to pump enough to supply the engine.
I would also check float level in the carb if it were mine.
Also might want to check to see how much fuel pressure you have if your able.
Could be the tank sock too I guess. I've never had to deal with one so don't know much about it.