According to this random link, Justin Roiland said:
The pilot, that was the worst. For some reason I was like, 'Rick has to burp every fucking line.' So I was in there for four hours recording Rick, and just swallowing air and doing every single line with a burp take. I left that studio with the worst stomach ache. I went home and laid in bed and thought I was going to fucking die or have to go to the hospital, it was seriously bad. And the irony is that we cut the radio play together and Harmon was like, 'There are way too many fucking burps in this,' and I was like, 'Oh fuck, you're right! This is disgusting.
Mainly, burping is painful to Roiland, and they probably decided that just a few very well placed burps could do better than some frequent eructing.