Notation:
Weights are numbered 1..12.
A x B  means weight set A against set B.
nL means weight n is light, nH means weight n is heavy

The solution:
(1,2,3,4) x (5,6,7,8)
=:
    (9,10) x (11,1)
    =:
        12 x 1
        <: 12L
        >: 12H
    <:
        9 x 10
        =: 11H
        <: 9L
        >: 9H
    >: analogous

<:
    (1,5,6) x (2,7,12)
    <:
        known: 1L or 7H
        1 x 12
        <: 1L
        =: 7H
    =:
        known 3L or 4L or 8H
        (3,8) x (11,12)
        <: 3L
        =: 4L
        >: 8H
    >:
        known: 5H or 6H or 2L
        (5,2) x (11,12)
        <: 2L
        =: 6H
        >: 5H

>: analogous