Solar synoptic maps of both He I 10 830 angstrom intensity and the magnetic field, which are observed by the Vacuum Telescope at National Solar Observatory/Kitt Peak from 2005 July to 2013 March are utilized to study relationship of He I intensity of the weakly magnetized chromosphere with the respective magnetic field strength. Strong absorption in He I intensity presents the butterfly-pattern latitude migration zone as active regions do, indicating that strong magnetic field corresponds to high-temperature structures of the active chromosphere. For He I intensity and magnetic field strength, their distribution at the time-latitude coordinate and their time series at each of the 180 measurement latitude are found to be significantly negatively correlated with each other in most cases. When a solar hemisphere is divided into three latitude bands: low, middle, and high latitude bands, and even after large magnetic field values not taken into account, they are still negatively correlated in most cases, and further when large magnetic field values are subtracted He I intensity varies more sensitively with magnetic field strength than the corresponding cases when large magnetic field values are not subtracted. He I intensity in the quiet chromosphere thus mainly presents a negative correlation with the magnetic field, and the heating of the quiet chromosphere is inferred to be caused mainly by small-scale magnetic elements.