There are two aspects to this question.
First, we must ask why government spending increased during this time. This happened in part because of the fact that the country was getting to be more committed to government domestic programs during this time. President Johnson’s “Great Society” programs were largely still in place. President Nixon was willing to do such things as creating the EPA. These sorts of government programs, of course, did much to increase spending. The increase also happened because of President Reagan’s commitment to greater defense spending. As the country became more committed to increasing both defense spending and social programs, the budget increased.
Second, we must ask why spending decreased with respect to GNP. Here, the answer is a little more obvious. If spending went up in absolute terms but declined relative to GNP, the only possible answer is that GNP increased. So, this happened because there was economic growth in the United States. Much of this growth occurred in the 1980s as the economy recovered after some very hard times in the 1970s.