我把这个句子转换一下：

Assignments are thus felt to be given added weight by the passage of time.

=Thus，it is felt that assignments will be given added weight by the passage of time.

that从句改为主动语态：

=Thus, it is felt that the passage of time will give assignments added weight.

由此可知，the passage of time是give的主语，assignments为间接宾语, added weight为直接宾语。改为被动句后，间接宾语作了主语，直接宾语成了保留宾语，原来的主语由介词by引出作状语（方式/施事状语）。按照汉语习惯将by翻译为“随着（时间的流逝）”是完全可以的。