In the long term, this can only happen when mortality is very high.
There are lots of things that seem to reduce the rate. We can consider education, birth control, taxes, child support, alimony, custody laws, religion, heathcare costs, daycare costs, education costs... and in the end it doesn't matter one bit.
None of that can possibly matter in the long run because the chance of having more offspring than normal is inheritable. You might point at birth control and ask how that fits in, but your ability and willingness/desire to use it is a mental trait that is at least partially inheritable.
You don't see how a child born to a lower class family of 7 might not be less reproductively fit than. A single child from the the same class?
Think of it this way, given what you know of class dynamics and sexual selection in humans, if your child had the choice of selecting between one in a random assortation, without knowing which was which, which one would be advantaged and why?
Let's work that through. We'll do a few generations, starting with 8 families of each type, with each type on their own separate isolated island to keep things simple. We start with 16 people on each island, half male and half female. Going generation by generation:
First: 56 kids, or 8 kids
Second: 196 kids, or 4 kids
Third: 686 kids, or 2 kids
Fourth: 2401 kids, or 1 kid
Fifth: 8403 kids, or extinction
Now, your idea that a child of a large family of 7 is less reproductively fit isn't going to help the low-reproduction families at all. They go extinct; they are thus clearly unfit. Unless the high reproduction families are losing about 5 of every 7 to early death, their population grows exponentially.
In reality, there are not separate islands. The resource exhaustion caused by the high-rate families will not just affect them. Everybody is effected. Even if the high-rate families are more affected, it isn't likely to stop them and anyway there is no saving the low-rate families from extinction.
There are lots of things that seem to reduce the rate. We can consider education, birth control, taxes, child support, alimony, custody laws, religion, heathcare costs, daycare costs, education costs... and in the end it doesn't matter one bit.
None of that can possibly matter in the long run because the chance of having more offspring than normal is inheritable. You might point at birth control and ask how that fits in, but your ability and willingness/desire to use it is a mental trait that is at least partially inheritable.
There is no escape from evolution.