Isn't discounting utility just a way of weighting future people less than current people?

We use the rationale that we can discount utility since people have a preference to consume soon rather than later; but when using a dynamic model over an infinite time frame how do we justify that someone living 200 years from would rather I consume 1 unit today as opposed to him consuming 3 units when he lives. This must be the case if all people are weighted equally.

I think you're right. It is weighting people today more than future people. Humanity does this all the time. Why?

What incentives are there in saving resources for tomorrow? Economically, there are none; the incentives exist only philosophically and sentimentally. There are no personal returns on investments made for future people, and non-economic incentives are much weaker and much less universal than economic incentives, as I'm sure you well know.

Meanwhile, people are able to feel less guilty about consuming resources because there is the idea that future generations will already benefit from any discoveries we make, and at the same time, they will benefit by learning from mistakes we make (assuming, of course, that these mistakes are not fatal). If we didn't consume these resources to improve our technology or advance our businesses or make our mistakes, then future generations would have themselves. At least now we can make them more prepared.

So there is a trade-off, and with the lack of economic incentives to save, I'm not sure there's very much motivation at all to "spend" additional resources on future generations. In a perfect world, things would be different, I'm sure, but as people who study economics, we know we cannot expect true altruism.
Discounting utility is not necessarily discounting future people vs current people.

It is discounting future utility vs. current utility.

What links the future and current is the financial sense of return on capital.

In your example: $1 (not the same as utility I know, but similar) can be invested and over time would generate a return and equal $3 in future time periods. Risk adjusted, that is why you would be indifferent

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