Using the starter numbers $2, 1, 4$ and $6$ you can get the largest total at the top of the pyramid if you place the largest numbers in the middle:
$1, 4, 6, 2$
$1, 6, 4, 2$
$2, 4, 6, 1$
$2, 6, 4, 1$
all produce a total of $33$.
Using the starter numbers $2, 1, 4$ and $6$ you can get the smallest total at the top of the pyramid if you place the smallest numbers in the middle - that produces a total of 19.
Justification: with $A, B, C$ and $D$ in the bottom row you end up with
$A + 3B + 3C + D$ at the bottom.
With $5$ tiers you can get the largest total at the top of the pyramid if you place the largest number in the middle and the smallest numbers on the outside - there are $4$ possibilities altogether:
$1, 3, 5, 4, 2$
$1, 4, 5, 3, 2$
$2, 3, 5, 4, 1$
$2, 4, 5, 3, 1$
With $5$ tiers you can get the smallest total at the top of the pyramid if you place the smallest number in the middle and the largest numbers on the outside - there are $4$ possibilities altogether.
Justification: with $A, B, C, D$ and $E$ in the bottom row you end up with
$A + 4B + 6C + 4D + E$ at the bottom.
With $6$ tiers you can get the largest total at the top of the pyramid if you place the largest numbers in the middle and the smallest numbers on the outside - there are $8$ possibilities altogether:
$1, 3, 5, 6, 4, 2$
$1,3, 6, 5, 4, 2$
$1, 4, 5, 6, 3, 2$
$1, 4, 6, 5, 3, 2$
$2, 3, 5, 6, 4, 1$
$2, 3, 6, 5, 4, 1$
$2, 4, 5, 6, 3, 1$
$2, 4, 6, 5, 3, 1$
With $6$ tiers you can get the smallest total at the top of the pyramid if you place the smallest numbers in the middle and the largest numbers on the outside - there are $8$ possibilities altogether.
Justification: with $A, B, C, D, E$ and $F$ in the bottom row you end up with
$A + 5B + 10C + 10D + 5E + F$ at the bottom.