Twitter was based on sms, the standard SMS character limit is 160. They used 140 so they could use the remained 20 chars for other purposes.
The GSM-7 alphabet is the most common one in use with SMS (or, at least, it was as UCS-2 is more common now with emojis and such).
160 is the number of GSM-7 characters.
160*7/8 = 140 which is the number of bytes in the userdata portion of the TPDU.