78 cases is probably not enough to run regression period, that said you would be in worse shape for every extra variable you add to your model. So the fewer the better.

The best answer to your question is to have theory that determines which you leave in and out. Some use stepwise regression instead, which is sharply objected to by many. Sometimes people will run a series of models with different variables and see which has the highest R squared or AIC. The problem with that approach is that the chances of making an error in the statistical test increases as you use the same data set to analyze different models (corrections such as bonferoni are utilized to address this).

Multiple regression is superior if more than one variable influences the dependent variable as seems likely here. Correlation does not address that issue.