Take off minima are usually no lower than 300 ft ceiling and 2000 m visibility but these can be reduced for qualifying aeroplanes.
If in a multi, the engine failure case must be considered such that the weather must permit a return for landing or the aeroplane must have fuel and performance to fly somewhere else and land.
In the first case, the take off minima is the approach minima (IAL or visual) at the DEP AD, which would usually be greater than 300 ft ceiling and 2000 m visibility. In the second case, the take off minima at the DEP AD is 300 ft and 2000 m (or lower for the qualifying aeroplanes).
If you've seen aeroplanes departing into weather that does not permit a landing, then either:
It's a single and the weather is at least 300 ft ceiling and 2000 m visibility or
It's a multi and the plan is to land at a different AD should an engine fail.
The reason 300 ft ceiling and 2000 m visibility is required even if proceeding elsewhere after engine failure is so the take off can be conducted safely. Room below the cloud and some sort of forward visibility is required to manoeuvre for a landing following an engine failure. The larger aeroplanes must meet performance, depending on jet/prop - number of crew, RWY lighting and equipment requirements to reduce the take off minima below 300 ft and 2000 m.