Recording a replay even for a few seconds on a big minecraft world (1+Gb) results in a replay file of 150+Mb.
Actually, the world is not that big, just not the I just loaded a new world.
Apart from the huge file size, the replay world is super laggy (I assume cause it loads everything), practically unusable.
It also takes a whole minute or more to save it after leaving the world, even if you recorded a few seconds!

Ok, without knowing how replay mod does its thing, I will take a guess that it's loading everything. Even though the replay is being recorded in a few adjacent chunks, it still seems to load everything.

Is there something to be done? Or it's just an unfortunate situation, where the whole world has to be loaded?

It is unfortunate indeed, cause one big strength of replay mod is: Very small replay files, that generally do not grow in size that much with replay duration.