High-bypass turbofans were introduced into the airliner market around 1970, when the first widebody jetliners were released (the 747 was first, followed in rapid succession by the DC-10, L-1011, and A300); however, narrowbodies continued to rely on low-bypass turbofans (primarily the Pratt & Whitney JT8D) for considerably longer. To the best of my knowledge, the first narrowbody powered by high-bypass engines was the DC-8-70 (a re-engining of the DC-8-60), which entered service in 1982; the first narrowbody built with high-bypass turbofans, the 757, did not enter service until 1983. As for the other narrowbodies of the time:
707, 720, 1-11, F28: No high-bypass version ever became available (although high-bypass versions of the 707 and 1-11 were proposed, they never entered production).
727: The only 727s that ever flew with high-bypass engines were four 727-100s reengined and renamed 727-100QFs in 1992.
737: The first high-bypass version, the 737-300, was only introduced in 1984.
DC-9: Stubbornly held onto the JT8D into the mid-1990s, only switching to high-bypass engines with the DC-9-90.
What kept the narrowbodies from immediately, or almost immediately, taking advantage of the greater power and lesser fuel consumption and noise of high-bypass turbofans?