I'm not sure why you're burping so much, I've never had that problem when smoking. As for the eyes, just use some Clear Eyes or Visene.
I burp too when i get high...maybe the weed is just relaxing some muscles and releases some stored gases...or something...i really don't know what happens...visine works for red eyes
maybe your swallowing some of the smoke as you inhale, a girl I know did that, burped infront of her mom and the smoke came out. I yawn lots when Im in a very relaxing high.
Ya, be cautious of swallowing smoke as it usually isn't too plesent and can cause smokey belches >_<.
