How does new Hampshire early primary affect the extent to which candidates campaign there?

It affects it a lot. Since New Hampshire votes first, it has an huge role in how candidates choose to spend their time and money campaigning, because if a candidate wins New Hampshire then they get a lot of buzz and free media coverage. An early win in New Hampshire generates excitement around the winning candidate, giving them momentum going into later contests. This is a problem because candidates make sure to craft their platforms to appeal to the interests of New Hampshire voters, who are mostly white, mostly live in rural areas, and tend to be wealthier than most other Americans. This means that campaigns end up talking about things that matter to white, rural, wealthy New Hampshire residents while ignoring issues that are important to other kinds of people in other parts of the country.