The 1997b paper goes on to say that "if publication bias is present, it is expected that, of published studies, the largest ones will report the smallest effects." But why is that? It seems to me that all this would prove is what we already know: small effects are only detectable with large sample sizes; while saying nothing about the studies that remained unpublished.
Also, the cited work claims that asymmetry that is visually assessed in a funnel plot "indicates that there was selective non-publication of smaller trials with less sizeable benefit." But, again, I don't understand how any features of studies that were published can possibly tell us anything (allow us to make inferences) about works that were not published!
Egger, M., Smith, G. D., & Phillips, A. N. (1997). Meta-analysis: principles and procedures. BMJ, 315(7121), 1533-1537.
Egger, M., Smith, G. D., Schneider, M., & Minder, C. (1997). Bias in meta-analysis detected by a simple, graphical test. BMJ, 315(7109), 629-634.