Asymmetric Resistance for Trunk Stability
When training in the gym, we tend to want to train one side of our body exactly the same as the other side, focusing on "symmetry."
If we curl a 25 pound dumbbell with our right arm, we try our best to perform the same number of reps with that same resistance using the left arm. When it comes to training for trunk stability, however, applying an asymmetric weight to each side may be more realistic and applicable to our everyday activities. If we are squatting or lunging to pick something up from the ground, many times the weight distribution, especially if it is an irregularly shaped object, may be more to our right or left side. One example is carrying grocery bags into the house from your car. You most likely do not weigh the bags and place the exact same amount in each hand. One hand always ends up carrying more. When walking with the bags, we still try our best to maintain a stable upright trunk so that we are not leaning toward the right or left. So why not incorporate this into training from time to time? It may not be that terrible to train each side with a different amount of weight.
Instead of Suitcase Dealifting the exact same weight on each side, start off with a heavier weight in one hand for one set, and then switch for the next set. The focus should be on performing the Deadlift without allowing your trunk to "give in" to the heavier side, but keeping your trunk upright.
Same thing with the Kettlebell Squat. Try a heavier weight on 1 side. Then switch sides for the next set
This can be done by just squatting with 1 kettlebell one 1 side, but then switch it up and use 2 different weighted kettlebells in order to apply a higher total amount of weight to your body.
Try a combo movement of a squat press using different weights. Now you must stabilize your trunk with asymmetric resistance while transitioning from the ground to standing to pressing overhead, all while not allowing your trunk to lose control
This is just another way of introducing various perturbations to your body in order to train it to maintain and maximize its stability