Brief Answer:
Read below.

Detailed Answer:
I read your question carefully and I understand your concern.

Weakness and dizziness are two of the most non specific symptoms in medicine, meaning they can have many different causes. A TIA by definition is transient (TIA stands for transient ischemic attack), but a stroke can be a cause. There usually are other manifestations though like weakness or numbness of the limbs on one side, speech issues, double vision or vision loss, coordination issues, confusion etc.
However there may be subtle deficits you have missed and given the fact that he's had 3 different strokes in the past which may leave behind some deficit it is often difficult to distinguish new manifestations even for us neurologists. These past strokes themselves may also be a source of fatigue, it is a common consequence of stroke.
Given that he is someone with a predisposition for vascular issues there may be also an issue of small vessel disease, not a single stroke but wide spread changes in the small blood vessels leading to damage, sort of diffuse XXXXXXX strokes.
Another explanation may be his alcohol consume. Long standing alcohol use may lead to brain atrophy in particular the cerebellum, the little brain, which is essential for balance. It may also cause peripheral neuropathy due to alcohol itself or to nutritional deficiencies which also may manifest with fatigue and balance issues.

So as you see the neurological explanations can be several. Of course other causes have to be considered like anemia, kidney issues, low thyroid function etc, but since you mention liver enzymes to be normal he's probably had blood tests as well. So he should be seen by a neurologist to be examined for neurological signs indicating a brain lesion or peripheral nerve issues and if new signs are found maybe need new brain imaging or nerve conduction studies.

I remain at your disposal for other questions.

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