Chester didn't have anyone he planned to share his theory with since it was just a theory. There was no way for him to know that Jack couldn't have children unless his ex-wife were to have one with another man but even then, they didn't know if Scarlet and Jack had stopped being intimate long ago and that was the cause.
He noted how nervous Beth became with the news. Biting at her nails which seemed like something she would frown upon. The realisation that there might be a way her lie would come out had to be settled in. The last thing Beth should have done was claim to be pregnant.
Chester thought that their arrangement would soon be coming to an end since this lie couldn't go on forever. With that, Chester considered taking his family to leave town so he could get away from the trouble he caused.