All the weekly and monthly tournaments are tiered - check the leaderboards. Most of them are free and don't pay out much.
There are some payed weeklies and monthlies, tiered, too.
Tournaments with reasonable payout (Ready-Gos) start at Pro level.
Alas, inspecting scores and whatnots, the winners seem to be extremely talented ppl or those who have re-started with new accounts. A few of them have advanced in level (not tier) by extreme patience or level boosts and are able to use premium equipment. Rumour has it that some might be illegal multi-accounters.
That said, it might be very difficult to contend there without any of these options.