How can I solidify a 2d shape so that the rim isn't solidified and the center is solidified the most ? (Think creating a dome from a sphere) I am trying to create a teardrop shaped Jewel such as this one.



The approach I wanted to take is the create a cross section of the jewel and model it from a circle as seen here:



and then solidifying it in some way which would make the center have the most height and the keeping the rim as edges. Think of it as solidifying with a factor of 1 in the center (or the point where I choose) and that factor gradually decreases until it reaches 0 at the outer edges where they are not given any thickness. 

I'm not ever sure that this would be the right approach, but it seems to be the easiest if I am able to find a modifier that created my desired effect.
A way to do that using a modifier is to shrinkwrap the jewel to a plane, using a weighted vertex group (the plane here is displayed in wireframe mode):



Select the vertices you want to move (all except the borders).

Go to weight paint. 

Validate 'vertex selection masking'

Enable X mirror

Then paint (add) the wanted vertices.

Once done, smooth the result.



After that, you can tune the influence in the modifier :





Following the comment, in order to use more easily a mirror, start from a circle, extrude inside then grid fill the inner part. That will allow you to have an edge loop or more around the jewel, so that you can connect easily the main part to the mirror center. Here is the kind of start that can be good for that :