I am confused by the line. By default, you do have a line connecting the ends of the interval as shown (made easier to see by choosing one of the animals from the local data filter):
If you are wanting to change the color of the line, you can change the color of the entire error bar (along with other elements of the error bar), by right-clicking the graph and choosing Customize.
I believe the nesting will be necessary because you are wanting to have each animal graphed separately. If you have 200 animals, you are going to need 200 error bars. Even your example is nesting, but you are making the nested variable much closer. JMP just provides the information on WHICH animal you are looking at, which is lost on your example. Further, your example is nice if the animals are quite different. But if they are very close in weight you may not see the intervals even be separated. Ultimately, the more levels/animals you have, the closer JMP will put them. If you double-click the axis you can see some items that you may wish to change to try to make them more legible.
Finally, if each measurement goes into a column, it is easy to get into the format that I used. You use the Tables > Stack Columns command. If you look at the Source script that was in my earlier post, you will see the exact command that was used from your example table. Reading the script should tell you how to fill out the interactive dialog box.
Dan Obermiller