Why is the voltage drop over my MOSFET so large?
The circuit as it appears now has a couple minor issues.
SPST has 4 pins and appears to be a DPST or SPDT with a LED?
Vgs must be 2.5 to 3x Vgs(th) max.for low RdsOn.
Yet Vg=Vd=~Vs so Vgs =0 assuming V+ is common.
No go. Vs must be grounded at Vbat- with Vd to low side load to pull down.
(Assuming your interfaces can tolerate this in the off condition.)