The old man, who was going upstairs, stopped and looked at us very suspiciously.

suspiciously 是形容词 suspicious 的副词形式，由 suspicious（怀疑的）加上副词后缀 -ly 构成。suspicious 来自动词 suspect（怀疑），加上形容词后缀 -ious 表示"具有...性质的"。suspiciously 表示"以怀疑的方式"，即"怀疑地"。