Speakers of the various English dialects may disagree as to whether or not the prepositional use of "on" is stressed in their part of the world, Yuichi, but the important thing for you to remember is that such differences do occur. So your dictionary is absolutely correct to prepare you for them.
The key factor, perhaps more so in American English, that determines whether a word is weak or stressed in individual speech is a matter of its importance to the speaker and/or its importance to the listener's understanding of the sentence. For instance, "It goes on" employs "on" as an adverb, a part of speech that very typically takes high intonation in English, even more so when it distinguishes one phrasal verb from another. Consider the differences between "Go up", "Go down" and "Go on" and you'll see just how important each final syllable is, which means that each of these words is usually stressed.
Now look at your other example, "There is an apple on the table". In this sentence "on" is employed as a preposition to form the adverbial phrase "on the table" and while the entire phrase functions as an adverb, word stress among its three syllables may vary. Everyone would agree that "the" takes a weak pronunciation, with "on" and "table" being more stressed, but the question is to what degree.
If someone is looking for the apple under the table, a speaker would likely say "No, it's ON the table", because "on" is now of greatest importance to the sentence. However, if someone is looking on the kitchen counter, a speaker would probably say "No, it's on the TABLE", because "table" is now the operative word.
To complicate things further, many American speakers prefer to drop intonation over nonoperative words rather than place an "unnaturally" high stress over key words, so what becomes most relevant is the contrast among syllables, rather than the more traditional stress of syllables. Hence "on the table" is very frequently pronounced in the US as "/ən/ the table", which confuses no one, since the apple could not possible be in the table.