It seems like the Bais Hillel had a tendency to be lenient in Halachic matters vs the Bais Shammai, it was a sort of a presumption to them in which they were almost always successful to back up with their methods of Derash (and the same goes for Bais Shammai regarding their stringency). Was it a principle the Bais Hillel believed in (perhaps it was based on "Deruchehu Darchei Noam")? or was it some kind of train of thought? We find the same pattern in the later Achronim. For example: R moshe Feinstein vs. Chazon Ish...
This is touched on in the sefer Kovetz Yesodos V'Chakiros in the ״לשיטתם-ביאור מחלוקות״ section, which attempts to codify and find consistencies in arguments among the both the Bavli and Yerushalmi or other personalities of Shas.
The sefer, basing itself on Sifrei Kabbalah and Chassidus (בספר לאור ההלכה ״לשיטות בית שמאי וב״ה) characterizes the methodologies of both Beis Shammai and Beis Hillel in the following way:
Beis Hillel judges cases according to the מציאות - the reality, therefore they judge with the midda of Chesed. This naturally leads to being more lenient.
Beis Shammai judges cases according to theory (i.e. Non practical), they judge using the midda of Din, which is more strict.
The author attempts to prove this suggestion from a plethora or sources, too numerous to recount here.