Shipbucket

People, can you please explain to me what were the functions of cruisers in interwar/WWII years? I cant understand it. They have weak armour, short-range cannons and their speed is not very high, too. I am a cruiser diletant, so, waiting for your explanation.
Especially I am interested in purpose of light and heavy cruisers.

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«A sea is not a barrier, a sea is a road, and those who try to use the sea as an instrument of isolation soon realize their foe has already put the sea into his own service.». - Alfred Thayer Mahan.

There is a site called Wikipedia, enter 'Heavy Cruiser' and 'Light Cruiser' in the search panel and it will tell you all you need to know about cruisers.

Early cruiser was tasked to protect larger capital ship with their fast firing guns and high speed, against torpedo boats and destroyer.

rest you find on wikipedia

Heavy cruisers were there to kill other cruisers. Light cruisers were for scouting and screening capitol ships (heavy cruisers and up) from destroyers.

Heavy cruisers are really second class battleships in the interwar years, created by the WNT/LNTs.
they are not limited (as much 1930-36) as real capital ships that you cant build (23-37) and nobody really thought they had sufficient battleships to cover all stations.
they do not have "have weak armour, short-range cannons and their speed is not very high" compared to any other ships you can make ?
they are stronger than anything they cant easily run away from apart from maybe a few BC (only HMS Hood and maybe the slower R&R or 3x Kongos)

Lights cruisers (not really counting 10,000t 6" treaty "lights" due to limits in LNT) are the natural descendants of old cruisers designed to fill all the tasks you don't need a battleship from as well as to provide fleet escort protection from DDs. Such as trade protection hunting AMC around the world.

Don't forget commerce raiding as well as trade protection.

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USN components, camouflage colors, & reference links (World War II only)

A cruiser is a type of warship. The term has been in use for several hundred years, and has had different meanings throughout this period. During the Age of Sail, the term cruising referred to certain kinds of missions – independent scouting, raiding or commerce protection – fulfilled by a frigate or sloop, which were the cruising warships of a fleet.

I think the answers you have had essentially say that the function of cruisers between the wars were the same as in WWI and before.
I suspect that your question could be reworded?
"Would it be possible for ships designed within the inter-war treaty limits to actually fulfil the traditional functions of cruisers?"
The answer to that lies in the history of naval actions in WWII. eg German 'pocket battleship' cruisers acting against trade, River Plate, Matapan, Bismarck & Scharnhorst pursuits; Glasgow & Enterprise against German destroyers Biscay 1943.
Then note how cruiser recce functions were taken over by aircraft carriers.
Cruisers were never satisfactory second class battleships since the days of sail when any warship sent on detached operations was termed a 'cruizer'.
Bismarck was actually acting as a cruiser on commerce raiding duty.