system
Given the following post, respond as if you're commenting on Reddit:
human
[Star Wars] How does the Death Star's mass not cause great effects on planets it is near?
gpt
First, unlike most stellar bodies, it's mostly hollow. The ship is made up of rooms, corridors, bays, vents, service tubes, and such. While it still has considerable mass, it's not as if it's a solid sphere of metals. 

Second, the entire ship has a lot of artificial gravity generators so the inside can be useful to species which are adapted to a gravity environment. You may have noticed in images and videos of either of the Death Stars that the orientation of the interior is not like a sphere, where people walk relative to the core, but is rather up and down, so people are all upwardly justified. This means that the entire station is made up of a massive network of gravity fields. The result is likely that the ship itself has far less gravitational force than it would if it didn't have artificial gravity. 

Finally, it would make sense for the engineers to attempt to compensate for any major gravity for the reason you imply, that the station could disrupt the gravitational balance of a system it enters. The Death Stars were designed to destroy worlds using its directed energy superlaser, not to very slowly destroy entire systems by changing the gravitational relationships between large bodies.