If your weed trimmer stalls when you tilt it, it might be out of gas. You thought of that already, so you added more, and the problem hasn't gone away. You're probably going to have to clean something because there either isn't enough fuel in the carburetor or there isn't enough air, and both are needed for proper combustion. The fact that the trimmer stalls only when you tilt it suggests that the fuel line isn't properly positioned inside the gas tank, and you may have to reposition or replace it.
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Stalling usually occurs because of problems with the fuel system. There could be a blockage in the carburetor, but hopefully, it's something simpler, like the air filter, gas cap, spark arrestor or fuel line.
Start With the Easy Fixes
Two of the easiest repairs you can make on a weed trimmer are to service the air filter and the spark arrestor. They both block air flow when they're dirty, and that can cause the engine to stall out. It won't necessarily happen only when you tilt the trimmer, but it's more likely to happen then than at other times.
The air filter is usually in front of or above the carburetor, and you access it by unscrewing a nut and removing a cover plate. You can usually do this without tools. The air filter is the first thing you'll see when you remove the cover, so pull it out, give it a good cleaning with soap and water and let it dry or just replace it with a new one.
The spark arrestor is a small screen between the carburetor and the muffler, and it usually has a handle to make it easy to pull out. This is designed to prevent fires by catching sparks before they emerge, but it catches all sorts of other stuff as well, and when it catches too much, it won't let air out of the carburetor. Pull it out and clean it with a wire brush.
Maybe the Gas Cap
The gas cap on a weed trimmer has a vent to prevent pressure buildup in the gas tank, and when this vent is blocked, the pressure could get strong enough to stop the gas flow. This isn't exactly an easy fix because you have to locate the vent opening and clear it with a piece of wire or by spraying WD-40 into it, and you might not be successful. It's best just to buy a new gas cap so you can eliminate the gas cap as the source of the problem. The cap has to match the trimmer, so be sure to get one manufactured for your model.
No Luck?... Probably the Carburetor
You've eliminated all the other possible causes except two. The next-to-last possibility is that the fuel line is too short. Look into the gas tank and you should see it extending out for about 2 inches. If it's short, it won't catch the fuel when you tilt the trimmer. It may have just pulled itself out of the gas tank, and if so, you should be able to push it back in. If not, replace it.
The last possibility is the carburetor. Perhaps you've been using bad fuel, you left gas in the tank over the winter or there's just a normal buildup of sludge. Remove the carburetor and clean it with WD-40. If necessary, you may have to disassemble and rebuild it or as a last resort, buy a new carburetor.