Why is the "Rocky" franchise particularly lampooned for its many sequels?

Numerous reasons, but mainly because of the Rocky franchise's popularity in the time frame you are looking at.

Rocky was hardly the first franchise with lots of sequels when it began releasing them in the 1980s, but it was perhaps the most popular. Unlike other franchises which experienced fast diminishing returns, Rocky took a slight dip with its first sequel, but then its third and fourth films each did better at the box office than the original. This popularity increased its cultural relevance and made it a preferred target for parodies.

Other franchises with lots of sequels--more than Rocky--went under the radar. For example, the Friday the 13th series was up to eight sequels (compared to Rocky's four) by the time Back to the Future II came out, but slasher horror movies are not generally a reference that will be enjoyed by the broad family audience targeted by the Back to the Future franchise. In addition, Friday the 13th was not ever the force at the box office that Rocky was, and it wasn't until 2003 that a Friday the 13th movie made as much at the box office as the first one did (and they had to combine it with the Nightmare on Elm Street franchise to achieve that). More people will recognize Rocky and its many sequels than would recognize Friday the 13th--it's simply more universal. The same could be said for the Police Academy franchise, which was up to six sequels by 1989, but the box office for everything after 2 was incredibly low.

In addition to going after the franchise that was most broadly recognized, the parody writers may also have chosen to go after Rocky because it was so iconic in the culture. It's easy and not very sporting to kick around the Police Academy movies. Taking on Rocky gives a parody more gravitas.

The James Bond series was up to 12 movies by the time Rocky's first sequel was released, but people tend not to look at those films as sequels of each other. The movies are pretty independent of one another, each one a stand-alone story featuring the same characters, but not in any kind of arc.

The other thing to consider is the dates of your parody sampling. Very popular franchises that are just as relevant and lucrative and popular as Rocky--Fast and the Furious, Avengers, etc--all came out long after the 1980s, where you selected your parodies. I suspect someone looking to make a similar joke now might make it a Fast and Furious joke.