With the preface that I'm not an expert in the history of either country and my familiarity with either is mostly post-1979, and that I obviously don't want to get into 20 year rule stuff, I think I can point to a few things.
Pakistan has historically viewed Afghanistan as a natural part of its regional sphere of influence. Many Pakistanis have also clearly believed that some or all of Afghanistan should simply be ruled by Pakistan. The very word "Pakistan" is actually an acronym for Punjab, Afghan, Kashmir, Sind, and BaluchisTAN, with the "I" added later. Moreover, the border between the two countries, the Durand Line, named for a British officer who surveyed the line in the late 19th century, is disputed by both countries. Looking at either country ethnically, it's not really clear where one should begin and the other end.
While Pakistan has viewed keeping Afghanistan within its sphere of influence as a result of history, ethnicity and religion, the power struggles within Afghanistan have provided ample opportunity for Pakistan's great rival, India, to try to back the other side of whomever Pakistan has supported or otherwise undercut their position. Pakistan in turn has tried to turn its relationship with Afghanistan against India, for instance through its program of deploying radical recruits from the Afghan refugee camps to Kashmir.
The most direct period of conflict between the two countries in recent years followed the Soviet invasion of Afghanistan in 1979, which Pakistan viewed as a direct threat to itself and took upon a program with enormous international support of driving the Soviets out, mostly by backing Islamist Mujahideen like Gulbudin Hekmatyar and others with various forms of covert aid, for which Pakistan was generally able to direct the funds. They tended to favor ideological and ethnic clients to the exclusion of others in the country, some of whom would go on to wield power there. So the ethnically-Tajik fighter Ahmed Shah Massoud did not gain that kind of patronage from Pakistan.
We're getting incredibly close to 20 year territory, but ultimately after the Soviets withdrew and towards the end of the civil war, Pakistan chose to give its support to the Taliban, and would ultimately be one of only three countries in the world (along with the Saudis and the UAE) who recognized the Taliban government.
Source wise, mostly from Steve Coll's Ghost Wars.
