I'm not convinced by the above. Maybe it's a regional thing, but as a native speaker (Manchester, UK) I would most likely take "looks heavier" literally - perhaps a bag that's bulging - whereas "seems heavier" is less specific and doesn't explain how you've come to your conclusion.
I agree there are some contexts where "looks" and "seems" are virtually interchangeable, but I'd say they tend to be more abstract sentences, where context makes it clear that vision is not the defining factor in one's judgement.
Hah, regional is right. I'm an English speaker of the Colorado, US variety.
So, you disagree that "My bag seems heavier." is a natural sentence, or just the generalization that vision isn't always required? The suggestion was not intended to be that there is no visual element in the evaluation of which bag is heavier, only that "looks" doesn't require visual evidence in all cases.
The bulging bag certainly did require visual appraisal. But I'm not sure how else one might guess weight without looking or feeling. Maybe it is exactly visual evidence that the thing is bulging that allows the "looks" in a non-abstract context? Quick poll (x3) got more "looks heavier" than "seems heavier" for US English Natives.
Both sentences are valid and natural. I just don't think their meanings are the same. So I feel the two words are not "interchangeable". Whether "lijkt" is a good translation of both "looks" and "seems" in this context, I don't know for sure, but Lenkvist's answer below seems reasonable.
I agree that the meaning of "looks" is not always literal, but there is a difference between the two sentences. Saying a bag looks heavier suggests the assessment is in some way visual. Saying it seems heavier allows the possibility that the judgement comes from some other means, such as lifting/pulling the bag.
In short, I think whenever you say "looks like", you could instead say "seems like"; but the reverse isn't true.