A tractor without added ballast can only put about 60% of its rated horsepower to the ground. Then it just spins the tires. Added ballast also makes for a more stable tractor. It'll stay on side hills better and the front wont rear up so much with a heavy implement on the back.
That said, you don't need ALL that weight. I would probably get rid of the fluid in the rear and keep the cast iron weights. With a heavy mower on the back you will want Some front weight.
I use my 3000 year round. A little plowing and discing deer plots and gardens in the spring, brush mowing in summer and snow removal in the winter. For all of the above I prefer to have some ballast on my tractor. You state you are somewhat new to this tractoring stuff and like many of us may find you have more uses for it than you originally thought. Example; I have a boom pole that goes on the 3 point. With no loader I use it a Lot for lifting things onto a trailer or into a pickup, etc. For that I'm real glad to have front weights. I have a finish mower too and have found that with front weight the tires cut the lawn less when turning. Or for plowing and snow removal, dragging logs, etc the tractor would be much less effective without rear weights.
If you do decide to sell your weights they will sell easily. Front weights go for about $200 in these parts. Rears sell well also but value depends on what type they are. A photo would help us determine value.
Here is a photo of a friend on my 3000 with original Ford bumper and weights. They are a bit hard to find.
When he comes up to my land I'd better take my turn on the mower first as when he gets on it l don't get it back till the job is done.