You need to set up a filter to stop this from happening. Here are the steps from Stacker Likefre:
For the copy of sent emails issue:
Quick fix: You can set a rule or filter on the blackberry account. Log on to your blackberry account.
a) Select "filters" on the account is doing this
b) Select "Add Filter"
c) On the filter name, choose any name you want
d) On the "Apply filter when" field, select "From" field
e) On the "contains" field, put your email adress
f) Select "Do not forward messages to handheld" and click save