Using doubly-clamped silicon (Si) microbeam resonators, we demonstrate sub-attogram per Hertz (ag/Hz) mass sensitivity, which is extremely high sensitivity achieved by micro-scale MEMS mass sensors. We also characterize unusual buckling phenomena of the resonators. The thin-film based resonator is composed of a Si microbeam surrounded by silicon nitride (SiN) anchors, which significantly improve performance by providing fixation on the microbeam and stabilizing oscillating motion. Here, we introduce two fabrication techniques to further improve the mass sensitivity. First, we minimize surface stress by depositing a sacrificial SiN layer, which prevents damage on the Si microbeam. Second, we modify anchor structure to find optimal design that allows the microbeam to oscillate in quasi-one dimensional mode while achieving high quality factor. Mass loading is conducted by depositing Au/Ti thin films on the local area of the microbeam surface. Using sequential mass loading, we test effects of changing beam dimensions, position of mass loading, and distribution of a metal film on the mass sensitivity. In addition, we demonstrate that microbeams suffer local micro-buckling and global buckling by excessive mass loading, which are induced by two different mechanisms. We also find that the critical buckling length is increased by additional support from the anchors.