The big problem seems to be that the encumbrance system completely disables some actions, it should make those actions much slower (so performed much rarely) rather than not allow them.
(The time units are just representing how much time passes until an action can be performed, and in reality everything happens simultaneously. Encumbrance, especially if still within the limit of what you can carry, should only make you slower or less efficient, and not prohibiting to ever fire your weapon)
I gathered a number of solutions for this problem I've seen in other turn based squad combat games:
1. Allow time units to go into the negative (and start the next turn with that much less TUs) if and only if the action is the first action in the current turn.
2. If you finished your turn with some TUs left (after subtracting reaction fire, of course), allow a tiny amount of it to carry over to the next turn. So you can perform your "expensive" action every other turn.
3. Having more random variety in stats. Why should an average soldier become stronger than any new recruit you hire after a few missions? With more varied stats, you could hire a weightlifter to carry your heavy equipment around, of course, his other stats might be terrible.
4. Firing is divided into mini-actions, so it does not always take the same amount of TUs. Movement always consumes the same amount of TUs, just as aiming, etc., so units with higher TUs are faster. However, squeezing the trigger should take the same time. (time does not equal time units, as faster soldiers can consume more time units in the same time it takes a turn) So squeezing the trigger is not a fixed cost, but a percentage of the total TUs the unit has. If I remember correctly, the original X-COM used this system, and Jagged Alleince also used a somewhat complicated variation of it. It might be far from the current concept, I only included it for the sake of completeness.
