I need to have 200-250 samples each second for 4-5 sec., but better will be for 10-12 sec.
Each data have time and a data value of 5 numbers(es. 200,00 kg).
Well, 20000 can be stored into an unsigned int (0 to 65535) ... I presume the weight isn't negative.
So that's 2 bytes. 4 lots of 250 samples is 1000 samples, so that's 2000 bytes.
What you could do is add an SRAM chip to extend the memory. Take all the samples, and then slowly (ish) write them to an SD card. Or send them via serial.
The Atmega328 is about a $5 chip. There's a limit to how much you can do with that if you are trying to do professional-style measurements. For example you could get a Mega which has more RAM.