Long comment:
Let's focus on one particular user, Alice, and on comedy movies, during a period of years $\{y_1, y_2, \ldots, y_n\},$ where $y_n$ is the most recent year. Assume Alice watched total $t_{i}$ movies during each year $i.$ Further more, she watched $c_{i}$ comedy movies during that year $i.$
To model Alice's preference of comedy movies, we can use the fraction $ \frac{\sum_{i = 1}^{n} c_i}{\sum_{i = 1}^{n} t_i} = \frac{\text{total number of comedy movies watched}}{\text{total number of movies watched}} $
To add more weight to recent years, you can use a weighted sum, and assign higher weights to recent years. In other words, Alice's comedy score would be: $ \frac{\sum_{i = 1}^{n} w_i c_i}{\sum_{i = 1}^{n} t_i} $ where, for example, $w_n = n, w_{n-1} = n-1, \ldots, w_1 = 1.$ This weight assignment intuitively says that if Alice watched a comedy movie recently then we are going to count it more than once.
You can use different weight schemes. For example, you can read about exponential weights here in this Wikipedia article on Moving Averages.