What data type is your column in table in SQLite database ?
I expect, that it is declared as TEXT or CLOB ?
Then is is expected, that such column can hold large textual string, which possibly can not be displayed in one row in TDBGrid.
If you know, that text can be displayed, you can use own event handler for TField
http://www.freepascal.org/docs-html/3.0.0/fcl/db/tfield.ongettext.html where you can return :
AText := Sender.AsString;