This question is related to What's the fewest weights you need to balance any weight from 1 to 40 pounds?
You had 4 weights to balance any weight from $1$ to $40$ pounds which is answered previously as $w_1=1$, $w_2=3$, $w_3=9$, $w_4=27$ where $w_1<w_2<w_3<w_4$
This time, we just need to balance any weight from $1$ to $30$ pounds with least amount of weight again. ($4$ as you guessed)
Strangely this time what is wanted is to maximize the total amount of weights with the maximum value of the minimum weight, $w_1$?
For example; $w_1=1,w_2=3,w_3=9,w_4=17$ is a solution to find all weight from 1 to 30. But $w_1=1$ is not the maximum value of $w_1$ that can get and $w_1+w_2+w_3+w_4=30$ is not the maximum total.