What's that sound?

Waht kind of deck do you have. Is it a Scout? 3 grams sounds pretty heavy for this kind of deck, what cart are you using? Could be a few issues collectively or on their own depending on your set up.

It sounds like mechanical noise, most likely microphony from the lid if you leave that on whilst playing? Better to remove it during use.

Otherwise it's maybe some form of acoustic feedback. Try tapping the plinth with the needle on the record in a run-out groove and see what kind of noise it makes. It shouldn't make any but if you can hear a hollow echo sound then try isolating you turntable more effectively.

Try moving the speakers further away. If you have a supsended wooden floor try putting the deck on it's own wall shelf. You can also try things like sorbothane isolating feet, marble or granite slabs as deadening supports..etc
All these things will improve the mechaical isolation of you deck and improve clarity and resolution allowing information to be more effectively extracted from the grooves without outside interference.

But if you already have your deck well set up along these lines and you still hear noise between tracks, especially if it is more apparent on some records than others you may just be hearing the original master tape.
Especially on old analogue recordings you will hear noticable hiss from the master, room tone from the studio, noisy pedals and compressors maybe and this will obviously vary with the recording. It's usuallly more obvious on classical recording than rock.

Check out whatever the manufacturer of your cartridge recommends as the maximum playing weight. Try using a styus balance like the one made by shure which is pretty cheap, but good, to set the tracking force.

The Scout has a unipivot arm as far as I am aware which are notoriously difficult to set up right. Maybe your dealer will help out. Get him to check the bearing and maybe recharge the oil as this can also cause rumble.
You can check this yourself by performing a "spin test". Take off the belt and top platter if it has one and spin the spindle. It should rotate freely without making any noise whatsover for at least several minutes before coming to a halt.
Certainly you shouldn't apply over the manufacturers recommended tracking weight on the cart as this can damage your records badly.

Are You SURE It Varies With The LP?

We have a tendency to change the volume when we change disks. Maybe you are hearing more rumble when you change the disk because you are changing the gain.

If you put the stylus on the disk with the motor off and you hear rumble, it is low frequency feedback, which is common.

If the noise goes away when the disk is stopped and the stylus is on the disk, it is the disk. Some very poor disks did have rumble on them and the only cure is a rumble filter in the phono stage or pre-amp.

You need to remove the lid when playing records, and hang the turntable on the wall on its own shelf. Standing it on a wood floor is a recipe for rumble.

A lot of my newer records are made on recycled vinyl and exhibit this noise floor issue. When the music is going it gets masked which is why the engineers justify using it. Plus it's a lot cheaper. I've read before that when they recycle records they don't remove the label or anything, so you've got bits of burned paper in your record. If it really bothers you stick to virgin vinyl on your newer records.

Oh yeah and a lot of "audiophile 180 gram" pressings don't specifically say virgin vinyl but seem to be ok.