I think they do. My father was a very good single parent while raising 3 girls and always gave his last dime to make sure we had the things we needed. Just as it is up to the mother to seek assistance or take the man to court, it is up to the man to do the same. Only when more men stand up and seek their equal rights under the law, will this nonsense about being weak fall by the wayside. Your child is more important than what others think or gossip about. A parent is a parent and should not be discouraged by outdated stereotypes when confronted with the need to seek assistance from the courts or otherwise.
The squeaky wheel gets the grease and there are many who would argue that single mothers are treated badly in certain areas of the country when seeking assistance, alimony, or child support. It's all dependent upon both your perspective and your will to be the best parent and provide the best that you can. Sometimes you must take some risks (being viewed as weak) that pale in comparison to providing a good upbringing for your child(ren). Nothing else is more important because as you know, the child is more important, than you even.