So if (chance of observation being correct) x (chance of claim being the cause of the observation) +/- (severity of being wrong) > (default threshold of certainty), you've got strong evidence. Naively it would then follow that everything else is weak evidence, but we also have a notion that evidence can be so weak as to imply now connection at all, so there seems to be for most people a "threshold of maybe", usually around 50% but as subject to personal scrutiny as threshold of certainty, that signifies something is conceivable, but further observations or explanations are necessary to move it beyond the threshold of certainty. I'd say this is where weak evidence lies: between ones threshold of certainty and threshold of maybe. Weak evidence is not worth believing in outright, but it's not worth discounting entirely either. Keep in mind also that "evidence" and "what is true" are necessarily separate; If we know a piece of evidence to be 100% true in supporting a claim, then the notion of evidence as something that convinces us of a claim breaks down, and such evidence is almost non-existent in our current universe.

So if (chance of observation being correct) x (chance of claim being the cause of the observation) +/- (severity of being wrong) > (default threshold of certainty), you've got strong evidence. Naively it would then follow that everything else is weak evidence, but we also have a notion that evidence can be so weak as to imply no connection at all, so there seems to be for most people a "threshold of maybe", usually around 50%, but as subject to personal scrutiny as threshold of certainty, that signifies something is conceivable but further observations or explanations are necessary to move it beyond the threshold of certainty. I'd say this is where weak evidence lies: between one's threshold of certainty and threshold of maybe. Weak evidence is not worth believing in outright, but it's not worth discounting entirely either. Keep in mind also that "evidence" and "what is true" are necessarily separate; If we know a piece of evidence to be 100% true in supporting a claim, then the notion of evidence as something that convinces us of a claim breaks down, and such evidence is almost non-existent in our current universe.

• Is the observation correct? Maybe the rock I observed on the first day is not the same as the one I observed on the second day, maybe I mistook something else for the rock atop the cliff, maybe the cliff I saw on the first day is an entirely different cliff from the one I went to on the second, or perhaps the cliff and rock are merely a philosophical contrivance and never really existed. At a certain level though, we would need to trust at least some of our senses to come to any conclusion, or we would end up in Decartes' "what is true?" dimension.
• What is the likelihood that the claim follows from the observation? In this case, perhaps the stone at the foot of the cliff is a totally different one, and the other stone remains at the top of the cliff. This contradicts the current observations, so it is unlikely. Perhaps a gnome teleported the stone from the top of the cliff to the foot of it. This is consistent with the current observations, but it is not a previously observed mechanisms for stones to travel between locations, so this is also unlikely. Perhaps the stone was moved slightly due to erosion, and then gravity pulled the stone to its current location at the foot of the cliff. This is consistent with the current observations, and the claim adheres to previous evidence that exceeds our threshold of certainty, assuming we've thrown stones and seen them fall back to the ground before so we can deem the claim likely to follow from the evidence.
• What are the consequences of our evidence being accepted but incorrect, or being rejected but correct? In this case, I may choose to reject the claim and associated evidence that stones above cliffs may fall, but if I reject it and the claim was right, my house would be damaged and I myself might be harmed. Conversely, if I choose to accept the evidence but it is wrong, there is not much resultant harm; My house wouldn't be under a cliff with rocks, but that is unlikely to be a hindrance to me. In this case it would be wiser to shift my threshold of certainty lower than it might otherwise be. You'll see this historically in some journals, that set a certain "confidence level" to serve as the bar for what is statistically significant, in some cases 95% or higher. 95% might be fine for a journal where the consequences of incorrect conclusions is low, but for say, the defect rate of aircraft parts, you'd want a confidence closer to 99.999% (1/10000 chance of a defective part), because the stakes are a lot higher.
• How skeptical or gullible am I? Where your threshold of certainty sits before taking consequences into account will largely depend on how skeptical/gullible of a person I am, and can range quite a bit between people.

• Is the observation correct? Maybe the rock I observed on the first day is not the same as the one I observed on the second day, maybe I mistook something else for the rock atop the cliff, maybe the cliff I saw on the first day is an entirely different cliff from the one I went to on the second, or perhaps the cliff and rock are merely a philosophical contrivance and never really existed. At a certain level though, we would need to trust at least some of our senses to come to any conclusion, or we would end up in Decartes' "what is true?" dimension.
• What is the likelihood that the claim follows from the observation? In this case, perhaps the stone at the foot of the cliff is a totally different one, and the other stone remains at the top of the cliff. This contradicts the current observations, so it is unlikely. Perhaps a gnome teleported the stone from the top of the cliff to the foot of it. This is consistent with the current observations, but it is not a previously observed mechanisms for stones to travel between locations, so this is also unlikely. Perhaps the stone was moved slightly due to erosion, and then gravity pulled the stone to its current location at the foot of the cliff. This is consistent with the current observations, and the claim adheres to previous evidence that exceeds our threshold of certainty, assuming we've thrown stones and seen them fall back to the ground before, so we can deem the claim likely to follow from the evidence.
• What are the consequences of our evidence being accepted but incorrect, or being rejected but correct? In this case, I may choose to reject the claim and associated evidence that stones above cliffs may fall, but if I reject it and the claim was right, my house would be damaged and I myself might be harmed. Conversely, if I choose to accept the evidence but it is wrong, there is not much resultant harm; My house wouldn't be under a cliff with rocks, but that is unlikely to be a hindrance to me. In this case it would be wiser to shift my threshold of certainty lower than it might otherwise be. You'll see this historically in some journals, that set a certain "confidence level" to serve as the bar for what is statistically significant, in some cases 95% or higher. 95% might be fine for a journal where the consequences of incorrect conclusions is low, but for say, the defect rate of aircraft parts, you'd want a confidence closer to 99.999% (1/10000 chance of a defective part), because the stakes are a lot higher.
• How skeptical or gullible am I? Where your threshold of certainty sits before taking consequences into account will largely depend on how skeptical/gullible of a person I am, and can range quite a bit between people.