When your calf is weak, things can dorsiflex too much sometimes. Maybe this is why you have Achilles tendinopathy. Maybe.
When we run, we either heel strike, midfoot strike, or forefoot strike. The literature is pretty clear on this now, that any one of them is not better than the other and there are many variables that need to be taken into consideration (even though many folks, who stopped reading the studies long after the barefoot craze began, will proclaim at the grave of their mother that rearfoot strike and anything but zero drop shoes are the root of all evil).
However, if you are a forefoot striker, the calf complex must be durable, strong and have enough endurance that when the foot strike occurs, that over time the complex does not allow the heel drop to become excessive or uncontrolled to the point that the achilles tendon proper exceeds its capacity to tolerate the drop, the stretch load capacity. It is more complex than this, because when the heel drops too much, too far, too fast and the arch is not durable enough, the metatarsals may dorsiflex too much and compromise the arch and stiffness of the midfoot, this can also have its complications. A weak calf can impact the rest of the foot. Remember, when the forefoot is engaged on the ground, and the heel drops in an uncontrolled fashion, we are increasing ankle dorsiflexion too, and this may not be welcomed during a stance phase of running where we are hoping for sufficient foot stiffness to load across it and propulse off of it.
This study showed that "analysis revealed that male recruits with lower plantar flexor strength and increased dorsiflexion excursion were at a greater risk of Achilles tendon overuse injury".
Intrinsic risk factors for the development of achilles tendon overuse injury: a prospective study.
Mahieu NN, et al. Am J Sports Med. 2006.