Use 'weariness' to describe exhaustion due to physical effort, long duration of activity, or lack of rest. The marathon runner's weariness was evident in his slow, dragging steps.
Pro Tip 2/3
Emotional Impact
It can also reflect mental or emotional exhaustion, not just physical tiredness. Her weariness was more from the emotional turmoil than the work itself.
Pro Tip 3/3
Beyond Sleepiness
Weariness implies a deeper level of tiredness than simply feeling sleepy. Even after a nap, the weariness from the hectic week lingered.