That's not true. Adam was punished just as bad as Eve was. God punished both of them for their sins. Adam tried to put the blame on Eve, but God knew better and punished both. Adam's punishment was that instead of having fruit given without any work, we would have to work in order to survive, while having to deal with other things.
I guess because Adam wasn't there? Both of them were equally tempted. Adam didn't even think to ask any questions, and the snake had persuaded Eve. That doesn't mean Eve was stupid, it just means she rebelled against God.
There's no "stereotype" that Christians have that says, "Well, a woman made a mistake, must make her gullible." The Bible gives many examples of men making mistakes as well. Think about Samson. He died because of his sins. Then you have kings that have endured God's wrath before. King David was a man after God's heart, but he was still punished for his mistakes. Woman are not the only ones who are gullible and weak. all of humanity is.