Two or Three Questions

[Bogertophis]

(1) We aren't seeing him so it's hard to say if he's underweight...but, you should be feeding him f/t rodents that are roughly the same diameter (thickness)
of his mid-body (before he's fed), or slightly less than that. How often are you feeding him? What is his age? From what you say, he sounds like he has a
good appetite...it's actually better to slightly under-feed a snake than it is to slightly over-feed them....it's healthier for them. BTW, BPs are more likely to go
off feed now & then as adults...they usually feed pretty well for the first several years (assuming husbandry is correct), & again, when it happens, it's normal.
Shakiness when feeding can be from the snake grabbing so tightly...also their muscles are strong when constricting, but not so much when they're reaching
upward, for example. Most snakes (BPs included) don't see that well...they use their heat-sensing pits to take aim at prey, then they fumble around to find
the right way to swallow it...yes, it's normal if they look a little dorky when doing this.

(2) A snake staying in the cool hide & hiding more is probably going into shed, & many times they save up their poo until they shed (sometimes they poo right
inside the old shed skin, as it comes off...which is very tidy of them, don't you think?) or shortly thereafter. Snakes just don't poo on any regular schedule, so
don't assume he is sick. When did he shed last? When a snake is nearing a defecation, their ventral area just above the cloaca may look somewhat puffy...it
helps to notice that since handling at that time may result in your snake taking a dump on you. Just saying...it's best avoided, lol. If he is going into a shed
cycle now, be sure to keep the humidity in his enclosure up for best results.