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'Reckon' in the UK usually has the sense of counting or calculating. There used to be little booklets called 'Ready Reckoners' which would list tables, so that you could see at a glance how much interest (say) £56.30 would accrue at 4%, or calculate tax rates on your income etc.
These seem to have disappeared into the same void as logarithm tables, now that people have cheap calculators.
I always thought that the american usage of 'reckon' involved a suppressed clause, so that 'I reckon' = 'I reckon/calculate that you are right'.
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