[rafs]

Solomons & Fryhle stated in their book that secondary alkyl halides are more likely to undergo SN2 reactions with weak bases and E2 with strong bases.

I understand SN1 and E1 occur better with weak bases than SN2 and E2... And I know it's better to avoid SN1 because other products may be found (if you can form a tertiary carbocation by rearrangement).

But if you don't have the possibility of rearrangement, why does secondary alkyl halides give mainly SN2 than SN1 with weak bases?

[Schrödinger]

We are comparing two competing reaction mechanisms here. When a base reacts with an alkyl halide, both S_N2 and E2 are possible.

But what property of the reagent (base) determines whether S_N2 or E2 happens preferentially?