There is a greater likelihood that a chord tone and an important beat will coincide. Also, in a C Major scale for example, there's a greater likelihood of C being that note. Next up, E and G are statistically equivalent in strength. After that D and A receive equal weight. Finally, F and B come in last.
The different rhythmic positions will have varying degrees of gravitational pull on the chord tones. In a measure of 4/4, the first beat of the measure has the biggest chance of occurring simultaneously with a chord tone. The third beat has only a slightly lower magnetic influence on chord tones. The 2nd beat of the measure is next in line. The fourth beat has lower attraction still.
Upbeats as in the "and of 1,2,3 and 4" have even less pull. 16th note subdivisions begin to function only as ornaments to the beat they neighbor and have no attraction on chord tones of their own.
Of course, if you put chord tones on every beat in every song, it will be boring. Sometimes playing chord tones in a melody on beat 1 is enough. Oftentimes, it isn't. If you have a case where that isn't working then you can put a chord tone on beat 3 as well to give that measure a little more unity. If there are no chord tones on beats 2 and 4 then it can create a nice tension and release through a few measures or a whole section.
In syncopated music it often sounds good to put chord tones off the beat so then you could have chord tones on the "and of 1" and the "and of 3". Or on most if not all of the off beats. This makes a nice contrast to sections where chord tones fall on the beat.
If you were working with a melodic series of pitches but with a new melodic rhythm, and if you wanted the chord tones to fall on the beat, (syncopated or not) you could repeat a note which was a chord tone that was falling on the "and of 2" for example so that beat 3 would also get that chord tone.
The other option would be to repeat the previous note instead which would push the onset of the chord to start on beat 3, not before.
Also, you can end on a weak rhythmic position in a chorus but then you probably don't want to end on a stronger rhythmic position in the verse. The strongest ending positions are...
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