remotely check amount of RAM on a computer using command line

Requires XP or later system: wmic memphysical list full, also wmic memorychip list full might provide you with some info you are looking for.

systeminfo /s:hostname will give you some basic memory statics if WMI isn't available on a remote machine:

C:\>systeminfo /s:hostname

...

Total Physical Memory:     3,062 MB
Available Physical Memory: 2,116 MB
Virtual Memory: Max Size:  2,048 MB
Virtual Memory: Available: 1,996 MB
Virtual Memory: In Use:    52 MB
Page File Location(s):     C:\pagefile.sys

To limit it to the Total Physical Memory and Available memory, you may use:

systeminfo /s:hostname | findstr "Physical"