I don't think so. On 16'ers it is possible to increase the wheel and tire size without
axle modifications. Ride height and
axle appear stock. OEM is a 3500# axle with 22 degrees down angle on the arms and standard
brakes. The axle arm appears to have some down angle under load, less than 22 degrees, but that's typical for an older trailer. My guess is it's original.
At 30+ years it could well be due for replacement, but it's not a given. Here are some things you can check:
(1) Raise one side of the trailer on the frame just behind the axle. As the frame rises note how much the hub drops relative to the top center of the wheel arch. Little or no movement indicate a "dead" axle, in which the rubber cords inside the axle tube have hardened.
(2) While the wheel is raised off the ground (make sure the trailer is securely chocked and blocked or hitched to your tug), grab the tire on opposite sides and give it a good shake. Everything should be nice and tight. Any looseness is reason to have the axle professional evaluated.
(3)Visually check wheel alignment. They should be straight and true, no camber or toe. Misalignment will show up as uneven tire wear, but that takes a while in regular use.
(4) The axle tube should have a slight upward bow to it and no evidence of impact damage.