One has to remember that antiship missiles by default, are all using active radar homing seekers or ARH. Meaning they carry the emitter on board. And that has been the basic concept all the way to the earliest, including Silkworms and Seersuckers. This enables them to be fire and forget, although more modern and longer ranged missiles, are now more like fire, then track updated in mid flight through a data link, then is only forget when the missile enters the terminal stage as it pops up over the horizon as the seeker goes active as it now has a LOS to the target.
SAMs like the HQ-9 work on SARH or TVM. That means the missile has no on board emitter of its own, and ship has to light the target with RF illumination for it to home in. For the HQ-9, or SAMs like the SM-2, Shtil, HQ-16, ESSM, S-400, to hit a surface target they all need to do it this way. The issue of this against a surface target is that the target needs to be line of sight with the ship, and so your effective range is only good up to the radar horizon only that can be reached by the shipboard emitters. Radar horizon means this is going to be short ranged, and its not going to engage over the horizon.
For the missile to have OTH, it needs to have an active seeker, like the Aster family, the Russian 9M96 family or the SM-6. Do note that by having a radar emitter on the missile means space used that is less for other things. And that can mean reduced warhead sizes. SM-6 is said to have only 64kg (wiki), which is small for a 1500kg missile. The HQ-16 is about 70kg for a 700kg missile. 9M96 family has 24kg size, while ESSM has 39kg. So if HQ-9 is turned into an active variant, without any change in size and weight, the warhead is going to end up smaller to allow for the emitter. If you are going to keep the warhead size, then it would be your propellant amount that will be reduced, which reduces your range or maximum speed. So in theory, HQ-9C, if that is the active variant of the missile, would be hard pressed to maintain the 180kg warhead, and may likely end up smaller. I have a theory that the 180kg warhead may only be for the first version of the HQ-9, where the larger blast can compensate for less accuracy and precision. Once the missile becomes more accurate and precise, the larger warhead may become redundant, you reduce the warhead size so you can increase propellant, which in turn can either give you a higher speed, for increased chances of interception, or a longer range. So its possible a longer ranged HQ-9 may have a smaller warhead for more propellant, and an ARH one an even smaller warhead. Other things like dual seekers, such as adding a heat seeker for OTH engagements, can potentially reduce the warhead size further.
Subsonic AshMs have a good ratio of warhead size to missile size. The Harpoon is about 221kg for warhead for a 691kg missile, the Exocet is about 165kg for a similar weight, and the YJ-83 either 165kg or a 190kg whicH I guess might be a roughly 700kg missile.
SAMs do travel at supersonic speeds, and one hitting a ship you will still incur kinetic damage. Due to the compression at the high speed impact, a warhead may explode with greater violence that is more like a larger warhead. Unspent rocket fuel will also add to the explosion. They will still hurt. SAMs used on surface ships are not a first option, but the option as a last resort still exists. Two AAW ships, once out of antiship missiles, can still duke it out by throwing SAMs at each other, which can end up as a win for the ship with more SAMs and will also involve SAM vs. SAM intercepts.
AshMs turned into LACMs are a different animal. Instead of ARH seekers, these missiles run on GPS, optical targeting and command guidance. Instead of radar, this means they got a TV camera on the nose, and there is someone controlling that thing.