Weed stems are extremely useful because they give you access to better resources in Grounded. However, even if you find them early in the game, you cannot cut them down to collect their resources. You need a second-tier item to do that, at least, the one you find that says “weed,” you do. You can alternatively locate a dandelion to chop down.
Dandelions are normally found in the areas with dry grass. Look for these in the areas where the grass is extremely yellow and nearly dying. These are also dangerous areas, so you need to be aware of your surroundings while wandering around here. When you find it, use your pebblet ax to take it down. It will take you several swings to remove, but once you do, you can pick them up as if they were grass planks and return to them to your camp.
These are large items that are great at crafting a variety of resources. You normally find dandelions a good distance away from the first field station, so prepare to wander around a bit before locating it and take it back to your camp. You want to use these pretty quickly, so don’t shy to stock up on these resources.