If you look forward / forwards it simply means you are looking ahead.
If you look forward you will see St Paul’s Cathedral.
Look forward to is a phrasal verb.
When you look forward to something, you feel happy and excited about something that is going to happen.
I always look forward to seeing my family and friends when I travel to England.
Correct: I’m looking forward to meeting you.
The verb is–> ‘to look forward to’ = ‘to anticipate’ (transitive = requires a direct object).
So, the direct object should be the gerund (noun) form of the verb ‘to meet’, i.e. meeting.
In contrast: “I’m waiting to meet you”.