Heavy weapons company means just that, in that had heavier weapons that the other infantry companies and were used to support the other companies.
In a typical German para regiment, there are three Battalions, each of four companies, companies numbered 1 to 12 with some extra, so a 13, 14 , 15 specialist companies ususally existed also.
Companies 4, 8 and 12 would be the heavy weapons companies, and used to support the others, in the case of your "schwere 4Kp" they would be supporting the 1st, 2nd and 3rd companies of their I battalion, FJR 9.
Heavy weapons would consist of the anti-tank (Pak), anti-aircraft (Flak) and anti-infantry (iG artillery) sections, to give you some idea of detailed content, following weapons would be available in this heavy company;-
-5cm and/or 8cm mortars
-Mg34 and/or MG42 on heavy tripods
-7,5cm Infantry guns (l iG)
-2cm flak 38's
-5cm Pak 38 and/or 7,5cm Pak guns
plus all the usual assortment of small arms, mines, rocket launchers etc.,
All divided into four or five troops (Zug) withn the company.
Not a lot different to any heavy weapons company of any other infantry unit, be they Marine, Heers, Waffen SS, Luftwaffe Feld, Combat Police etc.,
hope this helps,
cheers leonard paul