1.
Although possibly originating from the imitative of baby talk, this is in widespread use in the North of England and Wales as an informal "thanks" amongst adults.
2.
When a term originates in northern English dialects as "ta" appears to, I often begin by looking at nordic languages as much of northern England was conquered by the Vikings and the parts of the language endure both in words and in the overall sound - if you listen the geordie accent has a definite scandinavian cadence to it.
Looking at modern Danish and Norwegian we see that "Thanks" translates as "Tak" or "Takk" respectively, so it seems to me quite plausible that this provides an origin for "Ta".