To answer your last question first, yes. There are many resin wheel accessory sets availble as 'weighted tyres', from most of the major resin suppliers, covering many (but not all) of the most popular model types, and in most scales. I've just bought a set of 'True Details' wheels for a 1/48th scale Tempest - but only due to the kit wheels being plain and totally inaccurate.
There are two basic ways of achieving a 'weighted' or 'flat' look to model tyres, given that they are plastic and not rubber or vynl.
The simplest, and safest, is to simply file and sand a 'flat' spot on the tyre, and this is probably the most common method.
The other option, which will also create a slightly bulged look, is to press the tyre onto a heated surface, to flatten the area, and at the same time slightly bulge the side walls. As you can probably appreciate, the latter has to be done very carefully, and on a gentle heat, as there is a very real risk of ruining the whole component.
Depending on the scale of the model, a sanded flat spot is normally more than adequate, giving a 'footprint' and eliminating the perfectly round appearance. It's a good idea to take into account the type of aircraft, how the tyres looked on the real thing, and the conditions and environment. For example, a fully loaded Lancaster, standing on concrete, would show a slight bulge on the lower tyre wall, where a Spitfire, on grass, might not show any bulge, and the 'flat spot' might not be visible.
Here's an example on my unfinished 1/32nd scale Beaufighter. Only a very slight 'flat' has been filed onto each tyre, as the model will eventually be displayed on a base simulating a sand covered desert airfield. If it was to be on a hard standing, a slightly 'heavier' flat area would have been added. As the Beau didn't seem to exhibit much in the way of a 'bulge' to the tyres, no attempt was made to replicate this but, rather than using heat, a slight bulge could have been buit up and moulded using Milliput two-part epoxy putty, rather than risk the assembly being damaged by the heat treatment, or the joint of the two halves of the wheel separating, leaving an annoyong, and difficult to correct hole!
Hope this helps.