Would use of habitual past be considered "weak" writing or prose as opposed to simple past?
Perhaps by some. If so, it's the sort of opinion that can work perfectly well in guiding ones own style, but would make someone a fool if they started prescribing it as one everyone should follow.
Really, no common form is "weak" in and of itself, and developing a superstition that you should avoid some will in fact produce weaker writing because you'll be avoiding what would serve you best and using something less appropriate instead. Having personal preferences when forms are close to each other though, is reasonable, probably unavoidable, and part of what makes for ones personal style.
The simple past is generally terser, which can make it punchier, and so make it stronger in a lot of cases, but that's not always the case.
How does the simple past in the following sentence "He would cut weed and water the plants." without any preceding time expression e.g. "spend weekends" make a distinction between a repeated action/habit and a one-time action of cutting weeds and watering plants?
It doesn't (there are other possible additions that could make it clear, but on its own, it doesn't). In this regard it is less clear than the habitual past. Which would make it weaker, would it not?
Personally, I'm inclined to favour a combination of the two:
Jim would spend weekends at the farm. He cut weeds and watered the plants.
This has some of the terseness of the simple past, but also the more specific framing-in-time of the habitual past. With no further context than the two sentences, this seems to me stronger than either alternative (though not so much so that I'd consider someone crazy for disagreeing).
In a wider context, I might change my mind again.
(All this applies to the used to habitual past, too).