Researchers in British Columbia conducted a study that shows that women who did an hour or two of strength-training exercises per week had better brain function a year later than women who did only balancing and toning exercises.
The women were between 65 and 75 years old and the ones in the weights group improved their "executive functions" (defined as the ability to make decisions, resolve conflicts and focus on subjects without being distracted by competing stimuli) by an average of about 11% while the other group saw a decline of about half a percent.
This is one of a number of studies that suggest that regardless of your age doing weights training helps maintain and even enhance your mental functioning. I've been doing weights workouts for quite a few years now. Don't worry, you won't end up looking like those grotesque muscle guys (the secret of that look is injecting steroids). But you will look better, feel better, and even think better.