Breaking was born in a party, so naturally anything and everything that was there has influenced the way it looked and the feeling that's attached to the dance. The dances they'd do in a party affected the way breaking ended up looking. The reaction to the break section of the record provided by the DJ is what gave breaking its rhythm.
But the top rock that the original B-Boys did wasn't as complex as the B-Boys of today. According to many pioneers, it was more of a quick, sporadic intro to the ground moves about to happen next. Check out this clip below from Popmaster Fabel's channel, original B-Boy Lil Boy Keith, to get an impression. Many pioneers have also said breaking was originally done on top before the ground moves got more attention.
Lil Boy Keith
There are lots of things which have influenced top rocking. When more Puerto Ricans got involved with breaking, they added more vocabulary on top with their Latin influence and dance heritage.
James Brown's dance moves had similar influences. He was a great dancer and his steps on stage were wild and funky. Since breakers would dance a lot to his records, it was natural to also adapt some of his dance styles as well.
James Brown's dance moves on stage
The connection to and lineage from the rock dance, a gang originated dance style often also known as up rock, is definitely there as well. A lot of the steps are similar, yet the B-Boy and B-Girl way of doing them in slightly different, with a more bouncy and explosive feel. B-Boys and B-Girls would often mix the two dance styles of breaking and rocking to bring more burns and a battle feel to the solos. Once more OG rockers came back to the scene and said you can't really connect the two separate dance styles, the up-rock section kind of disappeared from breaking battles.
Hip-hop culture has always borrowed a lot from the masters of other fields of art and culture. The Nicholas Brothers, Fayad and Harold have been credited as influencers on some of the early B-Boys on top. Lindy hop is another dance style that's been said to influence the discipline a lot as well. Kung Fu movies were widely popular and you can see a lot of its influence in top rock as well, from Frosty Freeze's drunken style all the way to Ken Swift's infamous python style.
Ken Swift with the python style on Beat Street
The Nicholas Brothers
Since the days of old-school, the competition scene has developed and ended up influencing the way we see top rock today. A San Francisco-based event called Mighty 4 threw big-top rock battles which brought more attention on top again. There was even a movement called Breaklyn Rockers that connected the rock dance and top rock with a breaking approach by the organiser Paulskee and Jonny and Bionic Man. Yet a general idea was that in general top rocking has no jerks (rhythmic up and down movement specific to up rock).
Breaklyn Rockers Paulskee, Jonny and Bionic Man
A super-influential clique on the attention on tops is Mr Wiggles's and Ynot's Top Rock City. Top Rock City toured the world throwing top-rock battles and workshops for thousands to help people dance better and deepen their understanding about top. Soon even the biggest top style dance event Juste Debout (meaning just standing in French) in France included top rock battles in their categories of dance styles.
With such a big exposure as Juste Debout, a lot of dancers from other street style dances got interested in only rocking on top, neglecting the other elements of breaking such as footwork, power and freezes. That led to a lot of debates in the scene about different approaches. Should top rock be seen a dance style of its own or part of breaking? Can you learn how to top rock if you don't break? A general consensus among the scene is that top rock is definitely an important part of the dance style of breaking and should be trained as part of the whole dance style. To learn the proper groove and style of top rock, an understanding of the other elements of breaking is very important as well.