Will this dresser be able to hold a 125g tank?

This is only a test!

How about NY getting four of his largest friends to sit/stand on the dresser? That way its weight-bearing capacity could be tested without the risk of spilling 125 gal of H2O....Of course, there is still the risk of spilling 1000 lb of friends! And the dresser might not survive.
 
You'd want to figure on maybe 6 or 7 200 pounders up there and even then you're not taking into account the longterm effects of the stress. 120 gallons is a thousand pounds of water (ish). Its also about 200 lbs of tank. Add a little more for rockwork, substrate. Figure 1250 absolute minimum (All-Glass suggests 1400).

Its not built to handle that sort of weight. There's very little there to deal with racking. I think you'd find the draws jammed closed before long, and if it stopped there you'd be doing well.

It would be prudent to assume it'll fail at some point, either 10 minutes or 10 months after you fill it. What kind of odds can you live with? Higher than 0 would keep me up at night…
 
you could set the 125 directly on the floor and build a stand strong enuff to hold the 150 lb dresser over it.

then all you need is a bean bag chair to belly flop on and enjoy some serious tank gazing.
 
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