When delivering your signatures, consider your target and your objective. Have you called or met with your target to determine their position? Where do they stand on your issue? If your goal is to win over your target, you will likely want to impress them with the volume of people who agree with your position, as well as persuade them that these people matter.
If your target is already on your side, you will likely NOT want to take an adversarial tone. Instead you can call or write to the target and point to the number of signatures showing support for the issue.
Sometimes, all you need is a clear mandate for action. The petition and its signatures can be referenced in ongoing discussions with the target, to persuade them to take your cause to heart.
It is very important to remember that you are not the only person who cares about your issue. Each person who signs your petition and reads your updates is a potential ally. Help them become advocates. Make sure the information you post is accurate and up-to-date. Don't overwhelm the petition with lots of dry facts, but include a link where people can go for additional information and downloadable resources. The more people you can recruit to help—even informally—the more opportunities there will be for others to hear about your issue.