[Gelford]

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nh

how can you say it is wa/wb on the river? I do not think that means what you think it means.

wa/wb implies more cards to come and that either you or villain are drawing to <= 3 outs.

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It is a an NL expression, and the reason for using this here with no more cards to come is that if you bet, villian has the option to shove over your bet thus make you crap your pants or throw up in your mouth.
So therefore in such situations it is common to either check/call rivers ... to keep pot small and induce bluffs. (either that or blockbet)

Here such considerations are not as severe, but it is a reflex reaction of mine.

I tend to recall Mason and David advocating checking rivers oop in HEFAP, but it's more than a year since I read it, and it was written in weaktight FR days, so .... ?