Primaries are important in a variety of ways including giving popular opinion to superdelegates and caucuses. However, the system for determining each parties nomination differs not only by party, but state-by-state. How the final nomination will be determined is confusing and even changes periodically. One state may have an election this year, but held a caucus in previous years. So the weight is variable, not based on time but on process.
There is some debate about whether the Presidential Primaries are influential at this early time in the election season. However, as Trump's candidacy has shown, the Primaries are often a good "tell" of the future of politics. He has swept many early states and did well on Super Tuesday, which indicates that, agree of disagree, the Republican Party is going in a bold new direction.
The Presidential Primaries hold a lot of real weight this early in the race for the nomination because the primaries are indicative of who will win each parties nominations. Voting for the nominee is as important, if not more so, than the general Presidential election. People need to get this one right.
Yes, these primaries hold a lot of weight this early in the race. When a candidate gets off to a fast start, he or she gains a lot of momentum. When people see that one person is winning a lot, they get behind them. If they support other candidates, they will get discouraged and give up. Also, the media usually gets behind the front runners, and a lot of people follow the media's advice on who to vote for.