I have climbed the east side without ropes. As a climber, I do not reccommend this! The first 50 ft or so is slightly less than vertical and if you have no climbing experience, you will probably find that you wasted your time hiking up there only to be turned around well short of your goal. The last 30 ft or so is easy but VERY exposed. If you are not comfortable with heights, you will not enjoy that section.
Even if you don't use a rope on the way up, it is a good idea to bring one for the way down. Rappelling is much easier, faster, and safer than down-climbing. Be sure that you know how to use your gear.
Always wear a helmet! The rock on Weaver's Needle is very chossy. Chunks can dislodge when you least expect them to! I've witnessed this firsthand!
I hate to sound preachy, but I know of a lot of injuries and close-calls on Weaver's Needle.
"I'm not a vegetarian because I love animals; I'm a vegetarian because I hate plants." A. Whitney Brown