Is my floor gonna cave in?

if you're still going to be worried about it no matter what and you have access to the area underneath the room (crawlspace or something) you could get under there with some cinder blocks and shims and build up underneath to support the joists where the tank sits. really don't think you need to though.
 
2x16 could mean he has TGI JOISTS or truss joists both can be strong but often are used for spans greater then 16' "feet" 90% of all home costruction practices can handle a 75 gallon tank you should place the tank where you use the maxmum amount of joists that you can if the tank is only 12 to 18" wide then running paralell to the joists is not the best place because you will only have one joists supporting most of the weight and subfloor helping to distribute to the abutting joists. a metal stand is unadvisable if you have a house built cheaply the base of the legs could puncture the subfloor or simply distort it thus making the tank off level and tippy.
 
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