The $3000 of growth is taxable on conversion. When you recharacterize a Roth contribution to a nondeductible Traditional IRA, it changes the character of the IRA and the growth in the IRA. The original contribution is not treated as a Roth, but rather as a nondeductible TIRA. This saves you from the penalty of overfunding the Roth (because your income was too high); however, upon conversion, it means that the growth within the IRA is now taxable.
According to your example, you recharacterized your original $6500 Roth contribution into a nondeductible TIRA, but there were $9500 of total funds due to growth, which you then immediately converted back into a Roth. In this exchange, $6500 is considered to be a nondeductible TIRA contribution made as of the date you originally "contributed" it as a Roth (and would be the basis in the TIRA on December 31, 2017), and the $3,000 of growth will be taxed upon conversion into the Roth (since these funds grew tax-free, they are taxable upon conversion).
However, while the growth itself is taxable, the growth does not limit the amount of contribution you may make this year. If you wish to make another full back-door Roth contribution for 2018 (conversion being reported in 2020 for tax year 2019), you may do so.
This FAQ gives additional information on the difference between a recharacterization and a conversion: https://ttlc.intuit.com/replies/3300628
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