auxiliary
sentence-ending particle indicating speculation, volition, or invitation
Dialectal (Kantō, Tōhoku) equivalent of だろう or う/よう. Used at the end of sentences to express conjecture, will, or suggestion. Informal and regional.
明日は雨が降るべい。
It'll probably rain tomorrow.
一緒に行くべい。
Let's go together.
auxiliary
Archaic auxiliary equivalent to modern べき. Expresses obligation or strong expectation. Not used in modern standard Japanese.
See also: べき
昔の文献では「行くべい」が「行くべきだ」の意味で使われた。
In old texts, 行くべい was used to mean 'should go'.
Standard Japanese conjectural auxiliary. べい is its dialectal counterpart in Kantō and Tōhoku regions.
Derived from the classical auxiliary べし. The form べい is a dialectal and archaic variant, with the dialectal use surviving in Kantō and Tōhoku regions.