I can see on the Beyond Compare option list for the mergetool that one can specify to favor the right or the left side with -favorright or -favorleft option.
If I try to use it I get an error
$git merge master
[...](Actual merge with some conflicts)
$git mergetool -favorright
usage: git mergetool [--tool=tool] [--tool-help] [-y|--no-prompt|--prompt] [-O<orderfile>] [file to merge] ...
You are passing the -favorright argument to git. What you want is for git to pass that argument to Beyond Compare. This command will change your configuration for every future use of git mergetool.
$ git config --global mergetool.bc3.cmd "/usr/bin/bcompare -favorright \$LOCAL
\$REMOTE \$BASE \$MERGED"
You may need to substitute /usr/bin/bcompare for the correct path to the Beyond Compare executable on your system.