Yes - as I read it - they were far from Mordor - so weaker. Didn't have their horses with them, were on foot. And basically they are somewhat cowardly.
A bit like lions. Predators are quite cowardly - they only go in for the kill when they are sure that they won't be hurt themselves. Because it is important to you to keep in peak condition. A wounded lion, though still dangerous will soon starve. And even if there is only say a 1 in a 10 chance of being wounded, still, a lion won't take that chance because they make many kills and some day that chance will end up with them wounded and that's likely to be the end of them.
And predators are patient also. They lie in wait for the prey.
So I see it like that. They are not going to be in any hurry to strike someone down if they feel he is already injured and has no chance of survival.
They are also in the presence of a Dunedain, which they may feel, who is also carrying the broken sword Narsil, that was used to cut the ring from Sauron's hand - all though broken - and they would also feel the presence of the barrowdown weapons at least some sense of them - after all one of those weapons is part of the cause eventually of the Witch King's death.
And they are scared a bit of fire. I'm sure that wouldn't keep them off for long by itself. But on top of everything else it helps.
And also - Frodo himself - while wearing the ring - has immense power although he doesn't know it and doesn't know how to use it. Still, what if, in the moment, he somehow manages to draw on some resource to take command of them?
The safest thing is just to retreat now that he is wounded and they no longer have the advantage of surprise. And come in again when he is weak and barely alive, starting to turn into a wraith like themselves as a result of his wound and the shard of the sword inside him, and easily taken.
I'm speaking for the book here. Not the movie - which I haven't watched anyway, just bits of it.
Also I think there is another aspect. They thrive off fear. They are used to others being scared of them, and relish it. So when you are scared of them that gives them power. So Aragorn - by resisting them and by the power and confidence that is in him from his lineage - that changes the balance so they are no longer scary creatures intimidating a frightened hobbit - and that also I think weakens them at that point - with them also aware of the many leagues that separate them from Mordor.
Tolkein himself wrote:
"Their peril is almost entirely due to the unreasoning fear which they inspire (like ghosts). They have no great physical power against the fearless; but what they have, and the fear that they inspire, is enormously increased in darkness"
I think - a suggestion here - the main reason they are afraid of fire on weathertop is probably because it brings light in the darkness and counteracts fear. A cheerful fire like the one the hobbits were sitting around, after a damp and cold journey - is just the thing to help dispel fear.
In other situations such as in the battles, the fires increase fear. So it probably depends on the context.
And also Frodo is able to draw on some hidden strength himself - we know he is about to remove the ring, which few would do in that situation. Hobbits we learn have deep wells of strength. Sort of groundedness, a strength you get from the very ground. We learn that they are able to resist the power of the rings far longer than most other beings. So - that also will be a factor.
This - revealed suddenly to be surprisingly strong in character though apparently weak creature, carrying a ring that you know has total power over you, supported by an equally surprisingly confident stranger, regal in his bearing, wielding brands of fire (what will his next move be?), bearing the broken sword that cut the ring off Sauron's hand (I think they would sense that if just as a feeling of something hidden of great power), and surrounded by others who also have hidden ancient weapons of unknown power with powerful spells cast over them - spells that were specifically designed by the ancient spell casters for your destruction (as we learn later).
They live in the "other world" and wouldn't just see them as a bunch of brave but somewhat scared hobbits and a ragged and weatherbeaten man as others might. And are physically not especially strong themselves.
Then, the creature is wounded and can't last long (they don't know how tough hobbits are, and don't know that Aragorn has special healing powers over such sickness with athelas, might expect him to succumb within a day), they are way out in the wilds, several days journey from any help, you are far from Mordor with no support - and you have immensely long lives, have had many previous encounters with wounded creatures in similar if not identical situations - and the waiting game has worked for you many times in the past - and you can afford to be patient.