I use a truckers special 12 ton shorty hyd bottle jack under the axle tube next to the U bolt. The jack has a short legged channel that sits over the end of the jack and cradles the tube so the jack won't slip.
The axle tube on a std leaf spring suspension will not bend or crush or distort by jacking from it. Now I sure wouldn't place a jack towards the middle of the axle.
When I pulled trailers on the road I've jacked axles under fully loaded equipment trailers from 1750 lb axles on up to 10k axles with the old jack. This way all I'm lifting is one end of the axle instead of the whole side of the trailer.
Your trailer may weigh 7000 lbs on the axles or 1750 lbs per tire so it won't take much of a jack for that small weight
Now when at home I move my trailers up to the house and park them on the concrete pad in front of the garage. I can use my floor jack under the axle tube next to the U bolt.
Now if your trailer has a torsion axle system then you may have to jack the frame.
'03 Dodge 2500 Cummins HO 3.73 NV5600 Jacobs
'98 3500 DRW 454 4x4 4.10 crew cab
'97 Park Avanue RK 28' 2 slides