A way to bring the number of weighings down to about 1/2 would be to weigh all of them, record that weight (if it's 24 or 12, you know the weights). Then weigh 6, record those (again, 12 or 6, you know them). Then weigh 2 (4 or 2, you know). Then weigh 1. Based on that, you know the other. Repeat for the other sets of 2.

Worst case scenario, every set of 2 is mixed, which would lead to 12 weighings.

Let's take the scenario of 101101 101101:
{101101} 101101
{101} 101 101101
{1}01 101 101101
1 {0}1 101 101101
1 0 1 {1}01 101101
1 0 1 1 {0}1 101101
1 0 1 1 0 1 {101} 101
1 0 1 1 0 1 {1}01 101
1 0 1 1 0 1 1 {0}1 101
1 0 1 1 0 1 1 0 1 {1}01
1 0 1 1 0 1 1 0 1 1 {0} 1

A way to bring the number of weighings down to about 1/2 would be to weigh all of them, record that weight (if it's 24 or 12, you know the weights). Then weigh 6, record those (again, 12 or 6, you know them). Then weigh 2 (4 or 2, you know). Then weigh 1. Based on that, you know the other. Repeat for the other sets of 2.

Worst case scenario, every set of 2 is mixed, which would lead to 12 weighings.

Let's take the scenario of 101101 101101 and do a binary search:
{101101 101101}
{101101} 101101
{101} 101 101101
{1}01 101 101101
1 {0}1 101 101101
1 0 1 {1}01 101101
1 0 1 1 {0}1 101101
1 0 1 1 0 1 {101} 101
1 0 1 1 0 1 {1}01 101
1 0 1 1 0 1 1 {0}1 101
1 0 1 1 0 1 1 0 1 {1}01
1 0 1 1 0 1 1 0 1 1 {0} 1

Now let's try with groups of 2:
{101101 101101}
{101101} 101101
{10} 1101 101101
{1}0 1101 101101
1 0 {11} 01 101101
1 0 1 1 {0}1 101101
1 0 1 1 0 1 {10} 1101
1 0 1 1 0 1 {1}0 1101
1 0 1 1 0 1 1 0 {11} 01
1 0 1 1 0 1 1 0 1 1 {0}1

A way to bring the number of weighings down to about 1/2 would be to weigh all of them, record that weight (if it's 24 or 12, you know the weights). Then weigh 6, record those (again, 12 or 6, you know them). Then weigh 2 (4 or 2, you know). Then weigh 1. Based on that, you know the other. Repeat for the other sets of 2.

Worst case scenario, every set of 2 is mixed, which would lead to 12 weighings.

A way to bring the number of weighings down to about 1/2 would be to weigh all of them, record that weight (if it's 24 or 12, you know the weights). Then weigh 6, record those (again, 12 or 6, you know them). Then weigh 2 (4 or 2, you know). Then weigh 1. Based on that, you know the other. Repeat for the other sets of 2.

Worst case scenario, every set of 2 is mixed, which would lead to 12 weighings.

Let's take the scenario of 101101 101101:
{101101} 101101
{101} 101 101101
{1}01 101 101101
1 {0}1 101 101101
1 0 1 {1}01 101101
1 0 1 1 {0}1 101101
1 0 1 1 0 1 {101} 101
1 0 1 1 0 1 {1}01 101
1 0 1 1 0 1 1 {0}1 101
1 0 1 1 0 1 1 0 1 {1}01
1 0 1 1 0 1 1 0 1 1 {0} 1