So I'm looking to upgrade my 75 gallon to something around 125 gallons. Is that size tank still generally considered safe without extra support, or should I be concerned about that amount of weight causing serious deflection or worse. My house was built in '98, and the most likely location is on the 1st floor, against an exterior wall, perpendicular to the joists and about 6' on center from the corner of the house.

Some firsthand feedback would be great!

Thanks!

I have a 125 gal (6' long) in a house built in the early 1940s, then moved to this location in 1946. Construction on mine is VERY sturdy- full sized lumber, and lots of it.

If you have access under your house, go see how the joists were done.

Here in CA 2 x 6 doug fir @ 18" oc is common. Then 3/4" or thicker plywood as subfloor. Older construction (mine) used 2 x 6 as a subfloor.
This kind of construction will hold up a 120 gallon, short tank (4' long) even in the middle of the house- a friend of mine had this, and he is very careful to check this sort of thing.

Check the building strength of your house. Look for cracks in stucco, sheet rock, or plaster.
Hairline cracks are common, larger cracks suggest a problem.
Check that doors and windows open and close properly.
They may shrink and swell a bit in damp weather, but they ought to still open and close.

I researched into this exact question not too long ago.
Generally 125 gallon is regarded as the biggest tank you can keep safely without added floor support. Of course there are MANY factors that can come into play though.

But to keep things short, in your case a 125 gallon should be comfortably safe. Clearly you've done some homework on this so you do have things going for ya, which you mentioned (1st floor, against exterior wall, perpendicular to floor joists). I would say you could even go up to a 150 gallon with no problem, maybe even a 180. But again there are many factors though, so no one can say for sure.

A major sign of weight overload will be the sound the wood/house makes when it's about to snap (like a tree going falling), then you for sure have a major problem and need to drain the tank instantly.
But a sign to check for to see if the tank weight is slowly causing problems is to look if the floor sags (wall moulding will sit higher off the floor since floor is "sinking") as well as things Diana mentioned.

But it is not too hard to reinforce the existing flooring rather than buy expensive floor jacks if needed.

I had a 90 gallon (4 ft footprint) in the center of the house (house has cathedral ceilings so not sure how much different floor framing is) and after research, upgraded to a 150 gallon (only a 5ft footprint, not even a 6ft, so I could actually go to a 180 since the 6ft would distribute the more weight over more area). It does have a flat base stand though, not just a 4 legged stand, although shouldn't really make too much of a difference.
And that's not even the only tank in the room, got 6 others (55, x4 20s, 10)

I looked at the joists when I got home from work. They're 14" I-joists with a 2.5" flange and OSB web. 18" on center.

Unfortunately, the more I look at the room, the only practical location for a 6' tank would be parallel to the joists. There is, however, a perpendicular beam approx 5' on center from the new location, with a column approx 10' out from the load bearing wall.

Any more feedback would be great, but at this point, maybe its best to bring someone in to take a look.

What sort of material spans the I-joists?

If the tank is parallel to the I-joists, is the placement such that the front and the back would be over an I-joist? Then it would not matter what is in between them.

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One thing that should help - I would assume most 125 gallon tanks are atleast 18" deep (front to back). The I joists are 18" oc so, you should - thru careful measurements, be able to set the tank right on top of the joists as shown in Diana's left hand pic.