Question

1. The image stays a little bit longer in the brain than in the eye.

2. The image stays a little longer in the brain than in the eye.
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What is the difference between 'a little bit" and "a little"?

Answer 1

I would use neither, just say the image stays longer in the brain...

Now, your question. "little bit" is an idiom, from the use of coins, mainly Spanish in origin, in the colonial times. Coins were chopped up, often in eight pieces, and each piece was called a "bit", ie, 1/8 of a coin. For already small coins, chopping them up made very small pieces, ie, little bits. So the chopping was gradually modified for small coins, they were now only divided into one fourths...ie, thence we now have the "quarter" called "two bits".
Little bit means a small amount
Little means a small amount
So essentially, only a "little bit" of difference.