You don't have to give him gripe water for hiccups. Babies get hiccups all the time; it doesn't bother them like it bothers adults, and it's not a sign of indigestion or anything like that.
Also, some babies don't burp. Maybe he's just good at not swallowing a lot of air.
I've never known a baby that didn't start to experience bouts of fussiness at about two weeks of age. Almost all babies have a "witching hour" or two when they're just fussy and hard to comfort.
Colic is defined as up to three hours of fussing a day. And three hours can be LONG, but pediatricians say, tough as it is to deal with, it's not medically significant, nor is it usually anything they can treat. Instead, you swaddle a baby tightly, use a bouncer seat or a swing or even a sling, experiment with white noise (like a vacuum cleaner or the sound of the drier or a dishwasher), rocking motions, and you just get through it. (You might pick up a copy of "Happiest Baby on the Block" for some specific tips.)
If you're dealing with more than three hours of sustained fussiness a day, along with other symptoms of eating problems (projectile vomiting, latching on like he's starving only to pull away and cry, looking like he's spitting up but having nothing come out, etc), then it's time to let the pediatrician know so he/she can evaluate your son for reflux. My oldest daughter was a "silent spitter" (she did occasionally spit up an amazing amount, but she mostly swallowed it all, so it burned coming up and going down) with grade 3/4 reflux, and she cried--no exaggeration--for 14 hours a day, every day, until she was almost 4 months old. I seriously was at my wit's end. I called the nurseline in tears one night, and she listened to my daughter cry, and said, "Honey, that's not normal. You need to take that baby to the doctor. It's not anything you're doing; that baby needs help." She was right. We got a prescription for Prevacid, and she was a whole new baby.
Anyway, our pediatrician said that gripe water doesn't really work for anything except maybe gas. And she said that lots of it doesn't go through any kind of quality control or regulation, so you don't know exactly what you're getting. So we didn't use it. But, in theory, a single overdose shouldn't cause any damage.
If you're giving any med on a regular basis, you should be talking to your child's pediatrician about it.