You don't need to pinch off any flowers! May I add I've never seen a tomato plant that broke or dropped the tomatoes either, although in the wild, tomatoes grow as a sprawling vine, with the fruit often resting on the ground. The branches will thicken, and strengthen as the plant grows. Don't forget the tomatoes are pretty small at first and size up as the plant grows. Do you have the plants in a cage or otherwise supported upright?
If you want your plant to be more robust, maybe it can use more fertilizer? Show us a picture!