And Israel joined itself to Baal Peor, and the anger of Hashem burned against Israel.
Sanhedrin 64a — the nature of attachment to Peor (already partially on 25:5 TT; here on the joining itself).
English: A Tanna of the school of R. Yishmael taught: From where that idolatry is called “service”? As it is said, “And Israel joined itself to Baal Peor” — just as a bracelet does not move from its place, so idolatry does not move from its place.
Definition of avodah zarah from the verb of joining.
The “joining” of 25:3 is not a momentary slip — it is the tight, bracelet-like attachment that defines the gravity of the Peor sin.