how to launch weapon platform?

You don't. To go into more detail: They are sitting on your planet taking up cargo space and will fire when you are attacked. You don't need to do anything other than build them for them to work. I hope that made a little sense, I'm really not good at explaining things.

Think of them as Planetary Defense Centers, which you design. They're not intended to be mobile (though I suppose you could manufacture them on one planet and ship them elsewhere).

Exactly what you should be doing midgame. Build powerful weapon platforms on a developed planet, and put at least one on your colony ship. Ta-daa!! Instant defenses.

(good thing I didn't mention having mines in the cargo, that's too good a tactic to tell potential opponents)

"Genius is Simplicity" chris connors
"To win without fighting is best" sun tsu
those who think they know everything are annoying to those of us who do

A little bit of everything, mines, weapon platforms, fighters. If your colonizing a inhospitibal planet, having troops (i think fighters work) to boost moral is good.

SEV, more than a feeling.

As another variation on this theme, I prefer a few WPs with PD, a surveilance sat and fighters in the colony cargo. The fighters and the WP will work in space and surface defense and the surveilance sat will let you know if reinforcements are needed. This way, your planet can immediately start building facilities rather than defenses.

One of my colony ship designs is a large freighter with all three colony types, and it has a nice amount of cargo space, plus cloak and scanners for sneaking around in case it's been quite a few turns since I lasted scouted a system with a planet I want to colonize.
I usually load it with a Large WP (mixed weapons including a massive mount gun), 6 lg troops (2 w/ more guns, 2 balanced, 2 slow/heavily armored), 6 lg fighters (4 interceptors w/ afterburners, 2 with rocket pods or sm a-m torps) and a few lg sats (one lightly armed with scanners, plus one or more with mixed weapons).

Very handy to sneaking in a colony behind enemy lines, and making sure it is more than capable of fighting off basic attacks.

Some weapons have a range of 120ls (or greater), and and are handy in massive mounts on wps because they can equal or exceed the range of CSMs, making enemy ships unable to 'safely' bombard a planet with CSMs.
I nicknamed one of the weapons the BFG due to the name I gave to WPs/Sats mounting the weapon in SE IV.