Leveling up only increases HP, last time I checked.  It's a flat value per level up, I believe.

When a ship repairs, it repairs a set amount of hp, which can raise it over its max hp.  This is the effect you're seeing.

I don't have access to my GC2 at the moment, so I can't help you with the SB issue.

Thanks PUREVENOM, just what I needed. Except that it seems all types of starbases must have the same HP. I was hoping to make HPs be something like 500 for military, 300 for economy and influence, and 200 for mining and ascension.

There is another way to increase the HP of the starbase, that will let you set it to any arbitrary number.

First, open up the GC2Types.xml and add the following:

    <Hull Name="StarbaseHull">
        <DisplayName>Starbase Hull</DisplayName>
        <Description>Huge hulls are for true capital ships. They use 10 logistical points.</Description>
        <Cost>320</Cost>
        <SensorRange>4</SensorRange>
        <Size>150</Size>
        <HP>200</HP>  <!-- this is where you put in what HP value you want -->
        <Model>Huge_0</Model>
        <Thumbnail>Huge_0</Thumbnail>
        <Speed>1</Speed>
        <Category>Huge</Category>
        <Logistics>10</Logistics>
        <Tech_Requirement>ImpossibleTech</Tech_Requirement>
    </Hull>

Then, open up GC2Ships.xml and change to the following:

    <Ship Name="Starbase">
        <DisplayName>Starbase</DisplayName>
        <Model>Starbase</Model>
        <Description>Starbases expand your resources and extend your influence.</Description>
        <Tech_Requirement>ImpossibleTech</Tech_Requirement>
        <Component>StarbaseHull</Component>
        <Ability>Starbase</Ability>
    </Ship>

Out of curiosity, have you been able to get the AI to use these new hulls? I've read a few times about players modding in different kinds of hulls, and though about it myself, but the reports generally indicated that the AI wouldn't build them.