You just get used to the weight. You could do some excercises to strenghten your back. theres quite a few topics on that here. But like the others said, just keep good posture and just keep going. A BAD thing to do is locking your knees. Bend your knees just a little bit so everything can still flow so you dont pass out or whatever. But dont bend them too much to the ponit where its obvious.

Happy Drumming

sorry man...this guy is about your size and his drum is just a tad larger.....

http://www.msstate.edu/org/drumline/photo_albums/DrumCamp/IMG_0339.html

some of those basses look the same size to me..but this could be a camp for HS students and they have to bring their own drum and thats how that happened.

back on topic my bass was the size of either the bottom bass or next to bottom in that pic, i believe.
i had to go to the doctor right after camp started for shots last summer and i was told i was 5' 4" just like you.
you'll get used to the weight i marched bottom bass last year. i think mine was like a 22" or 24". but yes good posture as mentioned in other posts. you'll eventually adjust to the weight. best way to is to just wear the drum.

last year i'd wear the drum constantly (even when told to take it off) or atleast i did til i adjusted . im not tellin u to defy your section leader or instructor by no means for yours might get mad. mine didn't but i think it was because he realized what i was doing.

no use posting hear anymore my brother hasnt/wont ever get back on DLO

yeah, those are not the same size drums...I think we have 18, 20, 22, 24, 26, 28, 30, 34...those are definately not high schoolers either..hehe...thats the '07 MSU Bass Line; the rawest bass line in the land! hehe.

oh must be the distance from the camera that makes them look smaller to me haha but ok wow i was so off mine is the 4th bass so yea ..
ours is 16 18 20 22 24 now i believe

the only thing i can suggest is to ALWAYS practice with the drum on. never use a stand and you'll get used to the weight. something i tried was taking the drum home (i dont know if you have this option) and while it was at home i would use wire ties and attaced dumbells to the harness to make it heavier so then when i got to practice i was marching better and feeling more relaxed because the drum was lighter than i was used to.

I know the feeling cause i marched 4th bass in 3rd spot for 2 years...i just took an asprin daily and good luck