I never lost balance b/c of a tight grip, but when I started biking, late last year, I was really sore b/c of how tense I got on the bike. It's probably just going to take TITS (time in the saddle) to cure this one, you are going to become more comfortable each and every time you ride your bike, and you wont feel the need to hold on for dear life anymore! So, relax, know that if you fall, you'll just have to get up, and keep cycling, it gets better, and more fun every day!