In case anyone was considering taking this perk, it's not worth it. I have Dogmeat as a companion and his normal carry weight limit is 150 (pounds or kg?). The third level of Inspirational grants your companion additional carry weight. So with this perk, Dogmeat's carry weight goes up to 175.

Don't have data on carry weight of other companions or how much theirs goes up. Would be interested to know if it's always a 25 increase or a percentage increase of their base carry weight.

Since I've been using Strong Back #3, I don't even bother giving companions anything to carry.

If you are overburdened and you sprint, you will need to rest about every 10-20 seconds depending on your stats.

NOTE: Strong Back #3 doesn't stand on its own. Lots of things (SPECIAL, perks, equipment) can go into slowing the drain of AP, and speeding AP recovery.

I would say it's worth it if you are doing a lot of scavving early in the game. Now that I have Strong Back 4 it's not worth it.